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cp-templates/number/examples/factorial-inverse-in-linear.cc

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constexpr int N = 3e6 + 10;
ll fact[N], factrev[N + 1], s[N + 1];
void prep() {
fact[0] = factrev[0] = 1;
for (int i = 1; i < N; ++i) {
fact[i] = (fact[i - 1] * i) % MDL;
}
s[0] = 1;
for (int i = 1; i <= N; ++i) {
s[i] = s[i - 1] * fact[i - 1] % MDL;
}
factrev[N] = inverse(s[N], MDL);
for (int i = N; i; --i) {
factrev[i - 1] = factrev[i] * fact[i - 1] % MDL;
}
for (int i = 0; i < N; ++i) {
factrev[i] = factrev[i + 1] * s[i] % MDL;
}
}