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+20,MOD=(int)(1e9)+7;

int f[N],ie[N],n1,m1,n2,m2;

int power(int a,int b)
{
	int num=a,ans=1;
	for(int i=0;i<31;i++)
	{
		if(b&(1<<i)) ans=(1ll*ans*num)%MOD;
		num=(1ll*num*num)%MOD;
	}
	return ans;
}

int inverse_euler(int n)
{
	return power(n,MOD-2);
}

int ncr(int n,int r)
{
	return (1LL*f[n]*((1LL*ie[r]*ie[n-r])%MOD))%MOD;
}

void precompute()
{
	f[0]=1;
	for(int i=1;i<N;i++) f[i]=(1LL*f[i-1]*i)%MOD;
	for(int i=0;i<N;i++) ie[i]=inverse_euler(f[i]);
}

long long fn(long long n,long long m)
{
	long long ans=0;
	for(int i=0;i<=n;i++) ans=(ans+ncr(i+m+1,m))%MOD;
	return ans;
}

int main()
{
	precompute();

	cin>>n1>>m1>>n2>>m2;
	cout<<(fn(n2,m2)-fn(n1-1,m2)-fn(n2,m1-1)+fn(n1-1,m1-1)+3LL*MOD)%MOD;
}