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 ll mod=1e9+7;
#define mp make_pair
const int maxn=2e6+1;
int r1,c1,r2,c2;
ll fac[maxn+5];
ll inv[maxn+5];
ll C(int n,int m)
{
    //cout<<"C"<<n<<" "<<m<<"   :   "<<fac[n]*inv[m]%mod*inv[n-m]%mod<<endl;
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}
int cal(int l,int r,int x)
{
    return (C(r+1,x+1)-C(l,x+1))%mod;
}
int main()
{

    ios::sync_with_stdio(false);cin.tie(0);
    fac[0]=1;
    for(int i=1;i<=maxn;++i) fac[i]=fac[i-1]*i%mod;
    inv[0]=inv[1]=1;
    for(int i=2;i<=maxn;++i) inv[i]=(mod-mod/i)*inv[mod%i]%mod;
    for(int i=1;i<=maxn;++i) inv[i]=inv[i-1]*inv[i]%mod;
    cin>>r1>>c1>>r2>>c2;
    ll ans=0;
    for(int i=r1;i<=r2;++i)
    {
        ans+=cal(i+c1,i+c2,i);
        ans%=mod;
    }
    if(ans<0) ans+=mod;
    cout<<ans<<endl;
    return 0;
}