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constexpr ll MOD = 1e9+7;
inline ll pw(ll base, ll exp) {
ll res = 1;
while (exp) {
if (exp & 1) (res *= base) %= MOD;
exp >>= 1, (base *= base) %= MOD;
}
return res;
}
inline ll inv(ll x) { return pw(x, MOD-2); }
ll fact[MX] = { 1 }, ifact[MX] = { 1 };
inline ll nCr(int n, int k) { return fact[n]*ifact[k]%MOD*ifact[n-k]%MOD; }
for (int i = 0; i < N; ++i) fact[i+1] = (i+1)*fact[i]%MOD, ifact[i+1] = inv(fact[i+1]);
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