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>
#define inf 1e9+7
#define ll long long
#define clr(c) memset(c,0,sizeof(c))
const int M=2e6+10;
const int N=1e5+10;
const int mod=1e9+7;
using namespace std;
inline ll read()
{
	ll sum=0,b=1; char c=getchar();
	while(!isdigit(c)){if(c=='-') b=-1; c=getchar();}
	while(isdigit(c)){sum=sum*10+c-48; c=getchar();}
	return b*sum;
}
ll n,m,b,k;
ll r1,r2,c1,c2;
ll f[M+10],inv[M+10],Inv[M+10];
int main()	
{	
	ll i,j;
	r1=read(),c1=read(),r2=read(),c2=read();
	f[1]=1; inv[1]=Inv[1]=Inv[0]=1;
	for(i=2;i<=M;i++){
		f[i]=f[i-1]*i%mod;
		inv[i]=(mod-mod/i)*inv[mod%i]%mod;
	}
	for(i=2;i<=M;i++){
		Inv[i]=Inv[i-1]*inv[i]%mod;
	}
	ll ans=0; 
	for(i=c1;i<=c2;i++)
	{
		ans+=f[r2+i+1]*Inv[i+1]%mod*Inv[r2]%mod;
		ans-=f[r1+i]*Inv[i+1]%mod*Inv[r1-1]%mod;
		ans=(ans%mod+mod)%mod;
	}
	
	printf("%lld",ans);
	return 0;
} 