Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

* f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)



Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

* 1 ≤ r_1 ≤ r_2 ≤ 10^6
* 1 ≤ c_1 ≤ c_2 ≤ 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


r_1 c_1 r_2 c_2


Output

Print the sum of f(i, j) modulo (10^9+7).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include<iostream>
#include<cstdio>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<cmath>
#include<algorithm>
#define f first
#define s second
#define pb push_back
using namespace std;
typedef long long ll;
int const maxn=2e6+100;
int const mod=1e9+7;
ll num[maxn];
void init(){
	num[0]=num[1]=1;
	for(int i=2;i<maxn;i++) num[i]=num[i-1]*i%mod;
}
ll qpow(ll m,ll n){
	ll res=1;
	while(n){
		if(n&1) res=res*m%mod;
		n>>=1;
		m=m*m%mod;
	}
	return res;
}
ll C(ll n,ll m){
	return num[n]*qpow(num[m],mod-2)%mod*qpow(num[n-m],mod-2)%mod;
}
int main(){
	init();
	ll r1,r2,c1,c2;
	scanf("%lld%lld%lld%lld",&r1,&c1,&r2,&c2);
	ll res=C(r2+c2+2,c2+1)+C(r1+c1,c1)-C(r2+c1+1,c1)-C(r1+c2+1,c2+1);
	while(res<0) res+=mod;
	printf("%lld\n",res%mod);
}