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

// problem: "https://atcoder.jp/contests/abc154/tasks/abc154_f"

#include<bits/stdc++.h>
#define ll long long
#define p (ll)(1e9+7)
#define n (ll)(2e6+3)

using namespace std;

void calcFact(vector<ll>&V)
{
    V[0] = 1;
    ll i;
    for(i=1;i!=n;i++)
        V[i] = (V[i-1]*i)%p;
}

ll power(ll a,ll m)
{
    if(!m)
        return 1;

    ll b = 1;
    if(m%2)
        b = a;

    ll ans = power(a,m/2);

    ans = ((ans*ans)%p * b)%p;

    return ans;
}


ll nCr(ll a,ll b,vector<ll>&V)
{
    ll ans = (V[a] * power((V[b]*V[a-b])%p,p-2))%p;     // define

    return ans;
}


int main()
{
    ll r1,c1,r2,c2;
    cin>>r1>>c1>>r2>>c2;

    vector<ll>V(n);
    calcFact(V);      // define

    cout<<(nCr(r2+c2+2,c2+1,V) + p - nCr(r1+c2+1,c2+1,V) + p - nCr(r2+c1+1,c1,V) + nCr(r1+c1,c1,V))%p;        // define

    return 0;
}
