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 N=2e6+5,mod=1e9+7;
ll f[N],invf[N];
ll C(int n,int m)
{
    return f[n]*invf[n-m]%mod*invf[m]%mod;
}
ll c1,c2,r1,r2;
ll qpow(ll a,ll n)
{
    ll ans=1;
    while(n)
    {
        if(n&1) ans=ans*a%mod;
        a=a*a%mod;
        n>>=1;
    }
    return ans;
}
ll g(ll x,ll y)
{
    ll ans=0;
    for(int i=0;i<=x;i++)
        ans=(ans+C(i+y+1,i+1))%mod;
    return ans;
}
int main()
{
    f[0]=f[1]=invf[0]=invf[1]=1;
    for(int i=2;i<N;i++) f[i]=f[i-1]*i%mod,invf[i]=(mod-mod/i)*invf[mod%i]%mod;
    for(int i=2;i<N;i++) invf[i]=invf[i-1]*invf[i]%mod;
    scanf("%lld%lld%lld%lld",&r1,&c1,&r2,&c2);
    ll ans=g(r2,c2)-g(r1-1,c2)-g(r2,c1-1)+g(r1-1,c1-1);
    ans=(ans+mod)%mod;
    printf("%lld\n",ans);
}
