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 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();
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)
{
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[] 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 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[] 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)
{
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);
}
}
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);
}