Gym 101480F Frightful Formula（待定系数）题解

#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<cstdio>
#include<vector>
#include<cstring>
#include <iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int maxn = 2e5 + 10;
const int M = maxn * 30;
const ull seed = 131;
const int INF = 0x3f3f3f3f;
const int MOD = 1e6 + 3;
ll inv[maxn << 1], fac[maxn << 1];
ll ppow(ll a, ll b){
    ll ret = 1;
    while(b){
        if(b & 1) ret = ret * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return ret;
}
void init(int n){
    fac[0] = inv[0] = 1;
    for(int i = 1; i <= n; i++)
        fac[i] = fac[i - 1] * i % MOD;
    inv[n] = ppow(fac[n], MOD - 2);
    for(int i = n - 1; i >= 1; i--){
        inv[i] = inv[i + 1] * (i + 1LL) % MOD;
    }
}
ll C(int n, int m){
    if(m == 0) return 1;
    return fac[n] * inv[m] % MOD * inv[n - m] % MOD;
}
ll l[maxn], t[maxn];
ll dp[1000][1000];
int main(){
    ll n, a, b, c;
    scanf("%lld%lld%lld%lld", &n, &a, &b, &c);
    init(n + n);
    ll k = c * ppow(a + b - 1, MOD - 2) % MOD;
    ll ans = 0;
    for(int i = 1; i <= n; i++)
        scanf("%lld", &l[i]), l[i] = (l[i] + k) % MOD;
    for(int i = 1; i <= n; i++)
        scanf("%lld", &t[i]), t[i] = (t[i] + k) % MOD;
    for(int i = 2; i <= n; i++){
        ans = (ans + l[i] * C(n + n - i - 2, n - 2) % MOD * ppow(a, n - 1) % MOD * ppow(b, n - i) % MOD) % MOD;
//        printf("** %lld %lld\n", n + n - i - 2, n - 2);
    }
    for(int i = 2; i <= n; i++){
        ans = (ans + t[i] * C(n + n - i - 2, n - 2) % MOD * ppow(a, n - i) % MOD * ppow(b, n - 1) % MOD) % MOD;
    }
    ans = ((ans - k) % MOD + MOD) % MOD;
    printf("%lld\n", ans);
    return 0;
}
/*
4 3 5 2
7 1 4 3
7 4 4 8
*/
/*
3 2 3 0
1 1 1
1 1 1
*/