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 MAXN=2000010;
const int MOD=1e9+7;
int POW(int x,int k)
{
	int ans=1;
	for (;k;k>>=1,x=1LL*x*x%MOD) if(k&1) ans=1LL*ans*x%MOD;
	return ans;
}
int fac[MAXN],inv[MAXN];
void pre(int n)
{
	fac[0]=1;
	for (int i=1;i<=n;++i) fac[i]=1LL*fac[i-1]*i%MOD;
	inv[n]=POW(fac[n],MOD-2);
	for (int i=n-1;i>=0;--i) inv[i]=1LL*inv[i+1]*(i+1)%MOD;
}
int getC(int n,int m)
{
	if (n<m) return 0;
	return 1LL*fac[n]*inv[m]%MOD*inv[n-m]%MOD;
}
int cal(int n,int m)
{
	/*
	int sum=0;
	for (int i=0;i<=n;++i)
		for (int j=0;j<=m;++j)
			sum+=getC(i+j,i);
	return sum;
	*/
	return (getC(n+m+2,n+1)-1+MOD)%MOD;
}
int main()
{
	pre(2000005);
	int r1,c1,r2,c2;
	cin>>r1>>c1>>r2>>c2;
	long long Ans=cal(r2,c2)-cal(r2,c1-1)-cal(r1-1,c2)+cal(r1-1,c1-1);
	Ans%=MOD;
	if (Ans<0) Ans+=MOD;
	cout<<Ans<<endl;
	return 0;
}