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 mod 1000000007
using namespace std;

long long sx,sy,tx,ty;
const int MAX=3000005;
long long fact[MAX],fact_inv[MAX];

long long modpow (long long a,long long n)
{
	if(n==0) return 1;
	if(n%2)
		return (a%mod*modpow(a,n-1)%mod)%mod;
	else
		return modpow((a*a)%mod,n/2)%mod;
}

void make_fact()
{
	long long val=1;
	fact[0]=1;
	for(int i=1;i<MAX;i++)
	{
		val=(val*i)%mod;
		fact[i]=val;
	}
	fact_inv[MAX-1]=modpow(fact[MAX-1],mod-2);
	for(int i=MAX-2;i>=0;i--)
		fact_inv[i]=(fact_inv[i+1]%mod*(i+1)%mod)%mod;
}

long long comb(long long n,long long k)
{
	long long ret=1;
	ret=((ret*fact[n]*fact_inv[k])%mod*fact_inv[n-k])%mod;
	return ret;
}

int main()
{
	make_fact();
	cin>>sx>>sy>>tx>>ty;
	long long ans=0;
	for(int i=sx;i<=tx;i++)
	{
		ans+=comb(i+ty+1,ty);
		ans=ans%mod;
		ans+=mod-comb(i+(sy-1)+1,sy-1);
		ans=ans%mod;
	}
	cout<<ans<<endl;
	return 0;
}