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);
	}
}