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 int long long
using namespace std;
const int mod=1e9+7;

int r1,c1,r2,c2,ans=0ll;
int jc[10000005];

int quick_power(int a,int b)
{
	if (b==0)  return 1%mod;
	
	int res=1ll;
	for (;b;b=b>>1,a=(1ll*a*a)%mod)
	{
		if (b&1ll)  res=(1ll*res*a)%mod;
	}
	return res%mod;
}

int ny(int n)
{
	return quick_power(n,mod-2ll);
}

int C(int n,int k)
{
	int first=jc[n];
	int second=(1ll*jc[n-k]*jc[k])%mod;
	second=ny(second)%mod;
	
	return (1ll*first*second)%mod;
}

int find_sum(int l,int r,int k)
{
	int big=C(k+r+1,k+1);
	int small=C(k+l,k+1);
	return ((big-small)%mod+mod)%mod;
}

void get_all_jc()
{
	jc[0]=jc[1]=1;
	for (int i=2;i<=10000000;i++)  jc[i]=(jc[i-1]*i)%mod;
}

signed main()
{
	get_all_jc();
	
	cin>>r1>>c1>>r2>>c2;
	for (int i=r1;i<=r2;i++)  ans=(ans+find_sum(c1,c2,i))%mod;
	cout<<ans<<endl;
	
	return 0;
}
