ICPC2019NanchangIB.cpp

#include <bits/stdc++.h>
using namespace std;

#define int long long
const int N = 1010, P = 9999991;

int infact[N], fact[N];
int a[N], f[N];

int qpow(int a, int k) {
    int res = 1;
    while (k) {
        if (k & 1) res = res * a % P;
        a = a * a % P;
        k >>= 1;
    }
    return res;
}

int getsum(int x, int n) {
    // O(klog mod)
    if (x <= n) return f[x];
    int ans = 0;
    int fac = 1;
    for (int i = 0; i <= n; i++) {
        int now = f[i] * infact[i] % P * infact[n-i] % P * qpow(x-i, P-2) % P;
        fac = fac * (x-i) % P;
        if ((n-i) % 2) now = (P - now) % P;
        ans = (ans + now) % P;
    }

    return ans * fac % P;
}

void solve() {
    int n, m;
    cin >> n >> m;
    for (int i = 0; i <= n; i++) {
        cin >> f[i];
    }

    // f(n+1)
    int ans = 0, fac = 1;
    for (int i = 0; i <= n; i++) {
        int now = f[i] * infact[i] % P * infact[n-i] % P * qpow(n+1-i, P-2) % P;
        fac = fac * (n+1-i) % P;
        if ((n-i) % 2) now = (P - now) % P;
        ans = (ans + now) % P;
    }
    f[n+1] = ans * fac % P;
    for (int i = 1; i <= n+1; i++) f[i] = (f[i-1] + f[i]) % P;

    while (m--) {
        int l, r;
        cin >> l >> r;
        cout << (getsum(r, n+1) + P - getsum(l-1, n+1)) % P << '\n';
    }
}

signed main() {
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    fact[0] = 1;
    for (int i = 1; i < N; i++) fact[i] = fact[i-1] * i % P;
    infact[N-1] = qpow(fact[N-1], P-2);
    for (int i = N-2; i >= 0; i--) infact[i] = infact[i+1] * (i+1) % P;

    int T;
    cin >> T;
    while (T--) solve();

    return 0;
}