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;
#define N 3000005
#define MOD 1000000007 
int up=3e6,l1,r1,l2,r2,ans,fc[N],invF[N];
int inv(int x) {return x==1?1:1ll*inv(MOD%x)*(MOD-MOD/x)%MOD;}
int C(int x,int y) {return 1ll*fc[x]*invF[y]%MOD*invF[x-y]%MOD;}
int slv(int n,int m)
{
	int res=0;
	for(int i=1;i<=m;++i) res=(res+C(n+i+1,i+1))%MOD;return (res-m+MOD)%MOD;
}
int main()
{
	scanf("%d %d %d %d",&l1,&l2,&r1,&r2);--l1;--l2;
	fc[0]=invF[0]=1;for(int i=1;i<=up;++i) fc[i]=1ll*fc[i-1]*i%MOD;
	invF[up]=inv(fc[up]);for(int i=up-1;i>=1;--i) invF[i]=1ll*invF[i+1]*(i+1)%MOD;
	printf("%d\n",((slv(r1,r2)-slv(l1,r2)-slv(r1,l2)+slv(l1,l2))%MOD+MOD)%MOD);
	return 0;
}