P6078.cpp

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

#define int long long
const int P = 2004, N = 15;
int n, f[N];
map<int, int> F;

int C(int i) {
    int fact = 1;
    for (int j = 1; j <= n; j++) fact = fact * j;
    int res = 1;
    for (int j = 0; j < n; j++) res = (res * (n + i - j)) % (P * fact);
    assert(res % fact == 0);
    return res / fact;
}

int solve(int s) {
    int res = 0;
    for (const auto& [i, fi]: F) {
        int m = s-i;
        if (m < 0) continue;
        res = (res + fi * C(m)) % P;
    }
    return res;
}

signed main() {
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int a, b;
    cin >> n >> a >> b;
    for (int i = 0; i < n; i++) cin >> f[i];
    for (int S = 0; S < 1 << n; S++) {
        int idx = 0, val = 1;
        for (int i = 0; i < n; i++) {
            if (S >> i & 1) {
                idx += f[i] + 1;
                val = -val;
            }
        }
        F[idx] = (F[idx] + P + val) % P;
    }
    cout << (solve(b) - solve(a-1) + P) % P << '\n';
    return 0;
}