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;
const int N=2e6+5;
const int MD=1e9+7;
void add(int &x,int y) {
	x+=y;
	if(x>=MD) x-=MD;
	if(x<=0) x+=MD;
}
int f[N],inv[N];
int quick_pow(int x,int y) {
	int ans=1;
	while(y) {
		if(y&1) ans=1LL*ans*x%MD;
		y>>=1;
		x=1LL*x*x%MD;
	}
	return ans;
}
void init() {
	f[0]=1;
	for(int i=1;i<N;i++) f[i]=1LL*f[i-1]*i%MD;
	inv[N-1]=quick_pow(f[N-1],MD-2);
	for(int i=N-2;i>=0;i--) inv[i]=1LL*inv[i+1]*(i+1)%MD;
}
int cal(int x,int y) {
	return 1LL*f[x+y+2]*inv[x+1]%MD*inv[y+1]%MD;
}
int main() {
	init();
	int r1,c1,r2,c2;
	scanf("%d%d%d%d",&r1,&c1,&r2,&c2),r1--,c1--;
	int ans=0;
	add(ans,cal(r2,c2)),add(ans,cal(r1,c1));
	add(ans,-cal(r1,c2)),add(ans,-cal(r2,c1));
	printf("%d\n",ans);
	return 0;
}