2019 牛客多校 第一场 B、Integration

已知 ，求 在模1e9+7意义下的值。

保证 都是正整数，并且 各不相同。

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先解里面的式子，裂项相消。

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所以原式等于

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Code:

#include <bits/stdc++.h>

#define ll long long

using namespace std;

const ll mod = 1e9 + 7;

ll a[1005], a2[1005];

ll power(ll a, ll b)

{

    ll res = 1;

    while (b)

    {

        if (b & 1)

            res = res * a % mod;

        a = a * a % mod;

        b >>= 1;

    }

    return res;

}

int main()

{

    int n;

    while (scanf("%d", &n) > 0)

    {

        for (int i = 1; i <= n; i++)

        {

            scanf("%lld", &a[i]);

            a2[i] = a[i] * a[i] % mod;

        }

        ll ans = 0;

        for (int i = 1; i <= n; i++)

        {

            ll res = a[i];

            for (int j = 1; j <= n; j++)

            {

                if (i == j)

                    continue;

                res *= (a2[j] - a2[i] + mod);

                if (res >= mod)

                    res %= mod;

            }

            res = power(res, mod - 2);

            ans += res;

            if (ans >= mod)

                ans %= mod;

        }

        ans = ans * power(2, mod - 2) % mod;

        printf("%lld\n", ans);

    }

}