Interval product of zhinai sauce (prefix product + inverse element)

Topic link

https://ac.nowcoder.com/acm/contest/19483/A

Topic

Ideas

We require that the product of intervals be $1e9+7$ Submodule , Then this is a template of prefix product , And prefixes and similar , We just need to initialize $pre[0]$ by 1, Then when we do a division, we can't divide directly , Because there will be accuracy problems , So here we need to use Inverse element To help us with division

Code

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 1000000007

const int N = 1e5+10;


ll pre[N],a[N];
int n,m;


ll qpow(ll a,ll b) {
    
	ll ans =1;
	while(b) {
    
		if(b & 1) ans = ans * a % mod;
		b >>= 1;
		a = a * a % mod;
	}
	return ans;
}

ll inv(ll a) {
    
	return qpow(a,mod-2);
}


int main()
{
    
	pre[0] = 1;
	scanf("%d%d",&n,&m);
	for(int i = 1;i <= n; ++i) {
    
		scanf("%lld",&a[i]);
		pre[i] = pre[i - 1] * a[i] % mod;
	}
	int l,r;
	while(m--) {
    
		scanf("%d %d",&l, &r);
		printf("%lld\n",pre[r] * inv(pre[l-1]) % mod);
	}

	return 0;
}