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>
using namespace std;

long long MOD=1000000007;

long long fac[2000002],finv[2000002],inv[2000002];

void COMinit(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<2000002;i++){
		fac[i]=fac[i-1]*i%MOD;
		inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
		finv[i]=finv[i-1]*inv[i]%MOD;
	}
}
 
long long COM(int n,int k){
	if(n<k)return 0;
	if(n<0 || k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

long long a(int r,int c){
	long long ret=0;
	for(int i=0;i<=r;i++){
		ret+=COM(i+1+c,c);
		ret%=MOD;
	}
	return ret;
}

int main(){
	COMinit();
	int r1,c1,r2,c2;
	cin >> r1 >> c1 >> r2 >> c2;
	
	cout << (a(r2,c2)-a(r2,c1-1)-a(r1-1,c2)+a(r1-1,c1-1)+MOD*2)%MOD << endl;
	
	return 0;
}