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; 
typedef long long ll;
const int mod=1e9+7; 
const int maxn=2e6+3;
int r1,c1,r2,c2;
ll Finv[maxn+5],jc[maxn+5],ans;
ll modpow(ll x,ll n,ll mod)
{
	ll res=1;
	for(;n;x=x*x%mod,n/=2)
	if(n&1)res=res*x%mod;
	return res;
}
void init()
{
	jc[0]=Finv[0]=1;
	for(int i=1;i<=maxn;++i)
	{
	 jc[i]=jc[i-1]*i;
	 if(jc[i]>=mod)jc[i]%=mod;
    }
	Finv[maxn]=modpow(jc[maxn],mod-2,mod);
	for(int i=maxn-1;i>=1;--i)
	{
	 Finv[i]=Finv[i+1]*(i+1);
	 if(Finv[i]>=mod)Finv[i]%=mod;
    }
}
ll C(ll n,ll m)
{
	if(m<0||m>n)return 0;
	return jc[n]*Finv[n-m]%mod*Finv[m]%mod;
}
int main()
{
	init();
	scanf("%d%d%d%d",&r1,&c1,&r2,&c2);
	for(int i=r1;i<=r2;++i)
		ans=(ans+C(i+c2+1,i+1)-C(i+c1,i+1)+mod)%mod;
	printf("%lld\n",ans);
	return 0;
}