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 <bits/stdc++.h>
#define rep(i,n) for(int i=0; i<(int)(n); i++)

using namespace std;
using LL = long long;
const int Max_Num=2e6+10;
const LL mod=1e9+7;
LL F[Max_Num], Finv[Max_Num];

LL modpow(LL x, LL n){
	LL r=1;
	while(n){
		if(n&1) r=r*x%mod;
		x=x*x%mod;
		n>>=1;
	}
	return r;
}

LL modinv(LL x){
	LL m=mod, u=1, v=0;
	while(m){
		LL t=x/m;
		x-=t*m; swap(x,m);
		u-=t*v; swap(u,v);
	}
	u%=mod;
	if(u<0) u+=mod;
	return u;
}

void fact(){
	F[0]=1;
	rep(i,Max_Num-1){
		F[i+1]=F[i]*(i+1);
		F[i+1]%=mod;
	}
	rep(i,Max_Num) Finv[i]=modinv(F[i]);
}

LL calc(LL r, LL c){
	return F[r+c+2]*Finv[c+1]%mod*Finv[r+1]%mod;
}

int main(){
	fact();
	LL r1, r2, c1, c2;
	cin >> r1 >> c1 >> r2 >> c2;
	LL ans=calc(r2,c2)-calc(r1-1,c2)
	-calc(r2,c1-1)+calc(r1-1,c1-1);
	ans%=mod;
	while(ans<0) ans+=mod;
	cout << ans << endl;

	return 0;
}