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[] 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);
}
}