static void DFS3(int now, int parent,
List <int>[] graph, long[] res, int[] childs,
long[] pats, CaseCalculator calculator, long mask)
{
long pat = 1;
if (parent == -1)
{
pat = pats[now];
}
else
{
long parentVal = (res[parent] * calculator.Inverse(
calculator.Permutation(childs.Length - 1, childs[now] + 1))) % mask;
parentVal = (parentVal * calculator.Permutation(
childs[now] + 1, childs[now] + 1)) % mask;
parentVal = (parentVal * calculator.Inverse(pats[now])) % mask;
parentVal = (parentVal * calculator.Combination(
childs.Length - 1, childs[now])) % mask;
pat = (parentVal * pats[now]) % mask;
}
res[now] = pat;
for (int i = 0; i < graph[now].Count; i++)
{
int to = graph[now][i];
if (to == parent)
{
continue;
}
DFS3(to, now, graph, res, childs, pats, calculator, mask);
}
}
static void Method(string[] args)
{
int n = ReadInt();
List <int>[] graph = new List <int> [n];
for (int i = 0; i < n; i++)
{
graph[i] = new List <int>();
}
for (int i = 0; i < n - 1; i++)
{
int[] ab = ReadInts();
int a = ab[0] - 1;
int b = ab[1] - 1;
graph[a].Add(b);
graph[b].Add(a);
}
int[] childs = new int[n];
DFS1(0, -1, graph, childs);
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, n);
long[] pats = new long[n];
DFS2(0, -1, graph, calculator, pats, childs, mask);
long[] res = new long[n];
DFS3(0, -1, graph, res, childs, pats, calculator, mask);
for (int i = 0; i < n; i++)
{
WriteLine(res[i]);
}
}
static void Method(string[] args)
{
int k = ReadInt();
string s = Read();
long mask = 1000000000 + 7;
long[] divs = new long[1000000 + 100];
long[] divs2 = new long[1000000 + 100];
divs[0] = 1;
divs2[0] = 1;
for (int i = 1; i < divs.Length; i++)
{
divs[i] = divs[i - 1] * 25;
divs[i] %= mask;
divs2[i] = divs2[i - 1] * 26;
divs2[i] %= mask;
}
var calculator = new CaseCalculator(mask, s.Length + k + 100);
long res = 0;
for (int i = 0; i <= k; i++)
{
long val = calculator.Combination(s.Length - 1 + i, i) * divs2[k - i];
val %= mask;
val *= divs[i];
val %= mask;
res += val;
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
int q = ReadInt();
long mask = 1000003;
var calculator = new CaseCalculator(mask, mask + 100);
for (int i = 0; i < q; i++)
{
long[] xdn = ReadLongs();
long x = xdn[0];
long d = xdn[1];
long n = xdn[2];
if (d == 0)
{
WriteLine(calculator.Pow(x, n));
}
else
{
long baseVal = calculator.Multi(x, calculator.Inverse(d));
if (baseVal + n - 1 >= mask)
{
WriteLine(0);
}
else
{
WriteLine(calculator.Multi(
calculator.Permutation(baseVal + n - 1, n),
calculator.Pow(d, n)));
}
}
}
}
static void Method(string[] args)
{
int[] nm = ReadInts();
int n = nm[0];
int m = nm[1];
long mask = 1000000000 + 7;
List <int[]> factors = PrimeFactors(Abs(n));
var calculator = new CaseCalculator(mask, m + 100);
long res = 1;
for (int i = 0; i < factors.Count; i++)
{
res *= calculator.Combination(m + factors[i][1] - 1, m - 1);
res %= mask;
}
long minuses = 0;
for (int i = n < 0 ? 1 : 0; i <= m; i += 2)
{
minuses += calculator.Combination(m, i);
minuses %= mask;
}
WriteLine(res * minuses % mask);
}
static void Method(string[] args)
{
long n = ReadLong();
long[] xs = ReadLongs();
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, n);
long[] divs = new long[n];
for (int i = 0; i < n; i++)
{
divs[i] = calculator.Reverse(i + 1);
}
long[] sums = new long[n];
sums[0] = divs[0];
for (int i = 1; i < n; i++)
{
sums[i] = (sums[i - 1] + divs[i]) % mask;
}
long res = 0;
for (int i = 0; i < n - 1; i++)
{
long dist = xs[i + 1] - xs[i];
res += dist * sums[i];
res %= mask;
}
for (int i = 1; i < n; i++)
{
res = (res * i) % mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
int[] nm = ReadInts();
long n = nm[0];
long m = nm[1];
long[] array = ReadLongs();
long sum = array.Sum();
if (m < sum)
{
WriteLine(0);
return;
}
long mask = 1000000000 + 7;
var calculator = new CaseCalculator(mask, sum + n);
long res = 1;
for (long i = m + n; i > m + n - (sum + n); i--)
{
res *= i;
res %= mask;
}
res *= calculator.Inverse(calculator.Permutation(sum + n, sum + n));
res %= mask;
WriteLine(res);
}
static void Method(string[] args)
{
int n = ReadInt();
long[] array = ReadLongs();
Array.Sort(array);
long mask = 998244353;
long res = 0;
var calculator = new CaseCalculator(mask, 2 * n);
for (int i = 0; i < 2 * n; i++)
{
long tmp = calculator.Combination(2 * n - 1, n);
tmp *= array[i];
tmp %= mask;
if (i < n)
{
res += mask - tmp;
}
else
{
res += tmp;
}
res %= mask;
}
WriteLine(res * 2 % mask);
}
static void Method(string[] args)
{
long[] kn = ReadLongs();
long k = kn[0];
long n = kn[1];
long mask = 998244353;
CaseCalculator calculator = new CaseCalculator(mask, n + k - 1);
long allPat = calculator.Combination(n + k - 1, n);
long[] res = new long[2 * k - 1];
long prevPats = 0;
for (long val = 2; val <= k + 1; val++)
{
long pats = Min(val - 2, 2 * k - val) / 2 + 1;
if (pats == prevPats)
{
res[val - 2] = res[val - 3];
res[2 * k - val] = res[val - 3];
continue;
}
long seqCnt = Min(pats, n / 2);
long resTmp = allPat;
for (long i = 1; i <= seqCnt; i++)
{
long tmp = calculator.Combination(pats, i);
tmp = calculator.Multi(tmp,
calculator.Combination(k - 1 + n - i * 2, k - 1));
if (i % 2 == 1)
{
resTmp += mask - tmp;
}
else
{
resTmp += tmp;
}
resTmp %= mask;
}
res[val - 2] = resTmp;
res[2 * k - val] = resTmp;
prevPats = pats;
}
for (int i = 0; i < 2 * k - 1; i++)
{
WriteLine(res[i]);
}
}
static void Method(string[] args)
{
long[] nab = ReadLongs();
long n = nab[0];
long a = nab[1];
long b = nab[2];
long mask = 1000000000 + 7;
long[] pows = new long[40];
pows[0] = 2;
for (int i = 1; i < pows.Length; i++)
{
pows[i] = pows[i - 1] * pows[i - 1];
pows[i] %= mask;
}
long all = 1;
long tmp = 1;
for (int i = 0; i < 40; i++)
{
if ((n / tmp) % 2 == 1)
{
all *= pows[i];
all %= mask;
}
tmp *= 2;
}
all = (all - 1 + mask) % mask;
CaseCalculator calculator = new CaseCalculator(mask, Max(a, b));
long nA = 1;
long nB = 1;
for (long i = n; i >= n - a + 1; i--)
{
nA *= i;
nA %= mask;
}
for (long i = n; i >= n - b + 1; i--)
{
nB *= i;
nB %= mask;
}
all = (all - (nA * calculator.Inverse(calculator.Permutation(a, a))) % mask + mask) % mask;
all = (all - (nB * calculator.Inverse(calculator.Permutation(b, b))) % mask + mask) % mask;
WriteLine(all);
}
static void Method(string[] args)
{
int p = ReadInt();
int[] array = ReadInts();
CaseCalculator caseCalculator = new CaseCalculator(p, p - 1);
long[] combinations = new long[p];
for (int i = 0; i < p; i++)
{
combinations[i] = caseCalculator.Combination(p - 1, i);
}
long[] res = new long[p];
for (int i = 0; i < p; i++)
{
if (array[i] == 0)
{
continue;
}
res[p - 1]++;
long tmp = 1;
bool minus = false;
for (int j = 0; j < p; j++)
{
long delta = (combinations[j] * tmp) % p;
if (minus)
{
delta *= -1;
}
res[j] += p - delta;
res[j] %= p;
tmp *= i;
tmp %= p;
minus = !minus;
}
}
for (int i = p - 1; i >= 0; i--)
{
Write(res[i]);
if (i > 0)
{
Write(" ");
}
}
}
static void Method(string[] args)
{
int s = ReadInt();
long res = 0;
long mask = 1000000000 + 7;
var calculator = new CaseCalculator(mask, 5000);
for (int i = 1; i * 3 <= s; i++)
{
long remain = s - i * 3;
res += calculator.Combination(remain + i - 1, remain);
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
int n = ReadInt();
long mask = 1000000000 + 7;
var calculator = new CaseCalculator(mask, n);
long res = calculator.Permutation(n, n);
long minus = 0;
for (int i = 1; i <= n; i++)
{
minus += calculator.Combination(n - 1, i - 1);
minus %= mask;
}
res += mask - minus;
res %= mask;
WriteLine(res);
}
static void Method(string[] args)
{
int t = ReadInt();
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, 1000000);
for (int i = 0; i < t; i++)
{
int[] nmk = ReadInts();
int n = nmk[0];
int m = nmk[1];
int k = nmk[2];
int[] array = ReadInts();
Array.Sort(array);
long res = 0;
for (int j = 0; j + m - 1 < n; j++)
{
if (array[j + m - 1] - array[j] > k)
{
continue;
}
int bottom = j + m - 1;
int top = n;
while (bottom + 1 < top)
{
int mid = (bottom + top) / 2;
if (array[mid] - array[j] > k)
{
top = mid;
}
else
{
bottom = mid;
}
}
long len = bottom - j;
res += calculator.Combination(len, m - 1);
res %= mask;
}
WriteLine(res);
}
}
static void Method(string[] args)
{
long[] nk = ReadLongs();
long n = nk[0];
long k = nk[1];
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, n * 2);
long res = 1;
for (long i = 1; i <= Min(n, k); i++)
{
long tmp = calculator.Combination(n, i);
tmp = calculator.Multi(tmp, calculator.Combination(n - 1, i));
res += tmp;
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
int[] nxp = ReadInts();
int n = nxp[0];
int x = nxp[1];
int p = nxp[2];
int bottom = 0;
int top = n;
int upperCnt = 0;
int lowerCnt = 0;
while (bottom < top)
{
int mid = (bottom + top) / 2;
if (mid <= p)
{
bottom = mid + 1;
if (mid < p)
{
lowerCnt++;
}
}
else
{
top = mid;
upperCnt++;
}
}
long mask = 1000000000 + 7;
var calculator = new CaseCalculator(mask, n);
int lowers = x - 1;
int uppers = n - x;
long res = calculator.Permutation(lowers, lowerCnt);
res *= calculator.Permutation(uppers, upperCnt);
res %= mask;
res *= calculator.Permutation(n - 1 - lowerCnt - upperCnt, n - 1 - lowerCnt - upperCnt);
res %= mask;
WriteLine(res);
}
static void Method(string[] args)
{
int[] rcs = ReadInts();
long r1 = rcs[0];
long c1 = rcs[1];
long r2 = rcs[2];
long c2 = rcs[3];
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, r2 + c2 + 5);
long res = 0;
for (long i = r1 + 1; i <= r2 + 1; i++)
{
res += calculator.Combination(i + c2, i);
res += mask - calculator.Combination(i + c1 - 1, i);
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
long[] xy = ReadLongs();
long x = xy[0];
long y = xy[1];
if (2 * y - x < 0 || (2 * y - x) % 3 != 0 ||
2 * x - y < 0 || (2 * x - y) % 3 != 0)
{
WriteLine(0);
return;
}
long a = (2 * y - x) / 3;
long b = (2 * x - y) / 3;
long mask = 1000000000 + 7;
CaseCalculator calculator = new CaseCalculator(mask, a + b);
WriteLine(calculator.Combination(a + b, a));
}
static void Method(string[] args)
{
int[] nk = ReadInts();
int n = nk[0];
int k = nk[1];
int[][] lrs = new int[n][];
for (int i = 0; i < n; i++)
{
lrs[i] = ReadInts();
}
Array.Sort(lrs, (a, b) => a[0] - b[0]);
long mask = 998244353;
var calculator = new CaseCalculator(mask, n);
var que = new PriorityQueue <bool>();
int now = 0;
long res = 0;
for (int i = 0; i < n; i++)
{
int l = lrs[i][0];
while (que.Count > 0 && que.Top().Key < l)
{
que.Dequeue();
now--;
}
now++;
que.Enqueue(lrs[i][1], true);
if (now == k)
{
res++;
}
if (now > k)
{
res += calculator.Combination(now - 1, k - 1);
}
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
long[] nk = ReadLongs();
long n = nk[0];
long k = nk[1];
long[] array = ReadLongs();
Array.Sort(array);
long mask = 1000000000 + 7;
for (int i = 0; i < n; i++)
{
array[i] = mask * 10 + array[i];
array[i] %= mask;
}
if (k == 1)
{
WriteLine(0);
return;
}
CaseCalculator calculator = new CaseCalculator(mask, n);
long res = 0;
for (long i = k - 1; i < n; i++)
{
long tmp = array[i] * calculator.Combination(i, k - 1);
tmp %= mask;
res += tmp;
res %= mask;
}
for (long i = 0; i < n - k + 1; i++)
{
long tmp = array[i] * calculator.Combination(n - i - 1, k - 1);
tmp %= mask;
res += mask - tmp;
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
long[] nmk = ReadLongs();
long n = nmk[0];
long m = nmk[1];
long k = nmk[2];
if (n == 1)
{
WriteLine(m);
return;
}
long mask = 998244353;
CaseCalculator calculator = new CaseCalculator(mask, n);
long res = 0;
long[] pows = new long[n];
pows[0] = 1;
for (int i = 1; i < n; i++)
{
pows[i] = pows[i - 1] * (m - 1);
pows[i] %= mask;
}
for (long i = n - 1; n - 1 - i <= k; i--)
{
long tmp = m * pows[i];
tmp %= mask;
tmp *= calculator.Combination(n - 1, i);
tmp %= mask;
res += tmp;
res %= mask;
}
WriteLine(res);
}
static void DFS2(int now, int parent, List <int>[] graph, CaseCalculator calculator,
long[] pats, int[] childs, long mask)
{
long val = 1;
int childCnt = childs[now];
for (int i = 0; i < graph[now].Count; i++)
{
int to = graph[now][i];
if (to == parent)
{
continue;
}
long tmp = calculator.Combination(childCnt, childs[to] + 1);
DFS2(to, now, graph, calculator, pats, childs, mask);
tmp = (tmp * pats[to]) % mask;
childCnt -= childs[to] + 1;
val *= tmp;
val %= mask;
}
pats[now] = val;
}
static void Method(string[] args)
{
long[] nk = ReadLongs();
long n = nk[0];
long k = nk[1];
string t = Read();
long equals = 0;
long notEquals = 0;
for (int i = 0; i < t.Length / 2; i++)
{
if (t[i] == t[(int)n - i - 1]) equals++;
else notEquals++;
}
long mask = 1000000000 + 7;
long[] equalPats = new long[equals+1];
long[] notEqualPats = new long[notEquals+1];
CaseCalculator calculator = new CaseCalculator(mask, n);
long pow25 = 1;
for(long i = 0; i <= equals; i++)
{
equalPats[i] = calculator.Combination(equals, i);
equalPats[i] = calculator.Multi(equalPats[i], pow25);
pow25 *= 25;
pow25 %= mask;
if (i > 0)
{
equalPats[i] += equalPats[i - 1];
equalPats[i] %= mask;
}
}
long[] twoPows = new long[notEquals + 1];
twoPows[0] = 1;
for(long i = 1; i <= notEquals; i++)
{
twoPows[i] = twoPows[i - 1] * 2;
twoPows[i] %= mask;
}
long pow24 = 1;
for(long i = 0; i <= notEquals; i++)
{
notEqualPats[i] = calculator.Multi(
calculator.Combination(notEquals, i), twoPows[notEquals - i]);
notEqualPats[i] = calculator.Multi(notEqualPats[i], pow24);
pow24 *= 24;
pow24 %= mask;
}
/*
long[] notEqualSums = new long[notEquals + 1];
for (long i = 0; i <= notEquals; i++)
{
notEqualSums[i] = notEqualPats[i];
if (i > 0) notEqualSums[i] += notEqualSums[i - 1];
notEqualSums[i] %= mask;
}
*/
long res = 0;
bool haveCenter = n % 2 == 1;
for (long i = 0; i <= notEquals; i++)
{
long remain = k - notEquals - i;
if (remain < 0) continue;
if (!(notEquals == 0 && remain == 1))
{
res += calculator.Multi(notEqualPats[i],
equalPats[Min(equals, remain / 2)]);
}
if (remain > 0 && haveCenter)
{
long tmp = calculator.Multi(notEqualPats[i],
equalPats[Min(equals,(remain - 1) / 2)]);
tmp = calculator.Multi(tmp, 25);
res += tmp;
}
res %= mask;
}
WriteLine(res);
}
static void Method(string[] args)
{
int[] nk = ReadInts();
int n = nk[0];
int k = nk[1];
int[,] vals = new int[n, n];
for (int i = 0; i < n; i++)
{
int[] row = ReadInts();
for (int j = 0; j < n; j++)
{
vals[i, j] = row[j];
}
}
UnionFind rowSet = new UnionFind(n);
for (int i = 0; i < n; i++)
{
for (int j = i + 1; j < n; j++)
{
bool ok = true;
for (int l = 0; l < n; l++)
{
if (vals[i, l] + vals[j, l] > k)
{
ok = false;
break;
}
}
if (ok)
{
rowSet.Unite(i, j);
}
}
}
UnionFind colSet = new UnionFind(n);
for (int i = 0; i < n; i++)
{
for (int j = i + 1; j < n; j++)
{
bool ok = true;
for (int l = 0; l < n; l++)
{
if (vals[l, i] + vals[l, j] > k)
{
ok = false;
break;
}
}
if (ok)
{
colSet.Unite(i, j);
}
}
}
long mask = 998244353;
var calculator = new CaseCalculator(mask, n);
long res = 1;
for (int i = 0; i < n; i++)
{
if (rowSet.Root(i) == i)
{
int size = rowSet.GetSize(i);
res *= calculator.Permutation(size, size);
res %= mask;
}
}
for (int i = 0; i < n; i++)
{
if (colSet.Root(i) == i)
{
int size = colSet.GetSize(i);
res *= calculator.Permutation(size, size);
res %= mask;
}
}
WriteLine(res);
}
static void Method(string[] args)
{
long[] nm = ReadLongs();
long n = nm[0];
long m = nm[1];
long mask = 1000000000 + 7;
var calculator = new CaseCalculator(mask, m + 100);
long[] evenRevSums = new long[n + 10];
long[] oddRevSums = new long[n + 10];
for (int i = 0; i < n + 10; i++)
{
if (i % 2 == 0)
{
evenRevSums[i] = calculator.allInverses[i];
}
else
{
oddRevSums[i] = calculator.allInverses[i];
}
if (i > 0)
{
evenRevSums[i] += evenRevSums[i - 1];
evenRevSums[i] %= mask;
oddRevSums[i] += oddRevSums[i - 1];
oddRevSums[i] %= mask;
}
}
long res = 0;
for (int i = 0; i <= n; i++)
{
if (i % 2 == 0)
{
res += (calculator.Combination(n, i) * calculator.Permutation(m - i, n - i)) % mask;
res %= mask;
}
else
{
res += mask - (calculator.Combination(n, i) * calculator.Permutation(m - i, n - i)) % mask;
res %= mask;
}
}
res *= calculator.Permutation(m, n);
res %= mask;
/*
* for(long i = n - (m - n); i <= n; i++)
* {
* long tmp = calculator.Permutation(n, n - i);
* long selects = calculator.allPermutations[i];
* if (i % 2 == 0)
* {
* selects *= (mask + evenRevSums[i] - oddRevSums[i]) % mask;
*
* }
* else
* {
* selects *= (mask + oddRevSums[i] - evenRevSums[i]) % mask;
* }
* selects %= mask;
* tmp *= selects;
* tmp %= mask;
* res += tmp;
* }
*
* res *= calculator.Permutation(m, n);
* res %= mask;
*/
WriteLine(res);
}
static void Method(string[] args)
{
int[] nk = ReadInts();
int n = nk[0];
int k = nk[1];
long[] array = ReadLongs();
long mask = 998244353;
var calculator = new CaseCalculator(mask, k + 5);
long[,] pows = new long[k + 1, n];
long[] pow2s = new long[k + 1];
for (int i = 0; i <= k; i++)
{
for (int j = 0; j < n; j++)
{
if (i == 0)
{
pows[i, j] = 1;
}
else
{
pows[i, j] = pows[i - 1, j] * array[j];
pows[i, j] %= mask;
}
}
if (i == 0)
{
pow2s[i] = 1;
}
else
{
pow2s[i] = pow2s[i - 1] * 2;
pow2s[i] %= mask;
}
}
long[] sums = new long[k + 1];
for (int i = 0; i <= k; i++)
{
for (int j = 0; j < n; j++)
{
sums[i] += pows[i, j];
sums[i] %= mask;
}
}
for (int i = 1; i <= k; i++)
{
long val = 0;
for (int j = 0; j <= i; j++)
{
long left = sums[j] * calculator.Inverse(calculator.Permutation(j, j));
long right = sums[i - j] * calculator.Inverse(calculator.Permutation(i - j, i - j));
left %= mask;
right %= mask;
val += left * right;
val %= mask;
}
val *= calculator.Permutation(i, i);
val %= mask;
long sames = pow2s[i] * sums[i];
sames %= mask;
val += mask - sames;
val %= mask;
val *= calculator.Inverse(2);
val %= mask;
WriteLine(val);
}
}