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
#pragma GCC optimize(2)
#include <bits/stdc++.h>
#define int long long
#define MOD 1000000007ll
using namespace std;

int r1,c1,r2,c2,pw[2000010],rev[2000010];

inline int my_pow(int a,int b)
{
	if(b==0ll) return 1ll;
	if(b==1ll) return a;
	int res=my_pow(a,b/2);
	if(b%2ll==0ll) return (res*res)%MOD;
	else return (((res*res)%MOD)*a)%MOD; 
} 

inline int calc(int r,int c)
{
	int val=(pw[r+c]*rev[r])%MOD;
	return (val*rev[c])%MOD;
}

signed main()
{
	ios::sync_with_stdio(false);
	cin>>r1>>c1>>r2>>c2;
	pw[0]=1ll;rev[0]=1ll;
	for(int i=1;i<=r2+c2+5;i++){
		pw[i]=(pw[i-1]*i)%MOD;
		rev[i]=my_pow(pw[i],MOD-2ll);
	}
	int res=0ll;
	for(int i=r1;i<=r2;i++){
		int cur=calc(i+1,c2)-calc(i+1,c1-1);
		if(cur<0ll) cur+=MOD;
		res+=cur;
		if(res>=MOD) res-=MOD;
	}
	cout<<res<<endl;
	return 0;
}