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;
ll fpow(ll a,ll b)
{
    if(a==0) return 0;
    if(b==0) return 1;
    if(b==1) return a;
    //cout<<b<<'\n';
    ll t=fpow(a,b/2);
    t=(t*t)%mod;
    if(b%2) return (t*a)%mod;
    return t;
}
ll inv[2000050];

ll c(ll m,ll n)
{
    ll tmp=1;
    for(int i=m;i>m-n;i--)
        tmp=(tmp*i)%mod;
    for(int i=1;i<=n;i++)
        tmp=(tmp*inv[i])%mod;
    return tmp;
}
ll pre(ll r,ll l)
{

    return c(r+l+2,r+1)-1;
}

int main()
{
    for(ll i=1;i<=1000005;i++)
        inv[i]=fpow(i,mod-2);
    int r1,r2,c1,c2;
    cin>>r1>>c1>>r2>>c2;
    //cout<<c(5,3)<<'\n';

    ll ans=(pre(r2,c2)-pre(r1-1,c2)-pre(r2,c1-1)+pre(r1-1,c1-1))%mod;
    while(ans<0) ans+=mod;
    cout<<ans<<'\n';
}
