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>
#define rep(i,n) for(ll i=0;i<n;i++)
#define rep1(i,n) for(ll i=1;i<=n;i++)
#define repk(i,m,n) for(ll i=m;i<n;i++)
#define IOS ios::sync_with_stdio(false);cin.tie(0);
#define F first
#define S second
typedef long long ll;
typedef long double ld;
using namespace std;
const int MOD=1e9+7;
ll fp[2000005];
ll fpow(ll a,ll b)
{
    if(a==0) return 0;
    if(b==0) return 1;
    if(b==1) return a;
    ll t=fpow(a,b/2);
    ll ans=(t*t)%MOD;
    if(b%2==1) ans=(ans*a)%MOD;
    return ans;
}
ll comb(ll n,ll r)
{
    ll ans=1;
    for(ll i=n;i>n-r;i--) ans=(ans*i)%MOD;
    rep1(i,r) ans=(ans*fp[i])%MOD;
    return ans;
}
ll total(ll a,ll b)
{
    return comb(a+b+2,a+1);
}
int main()
{
    ll r1,r2,c1,c2;
    rep1(i,1000005) fp[i]=fpow(i,MOD-2);
    cin>>r1>>c1>>r2>>c2;
    ll ans=(total(r2,c2)-total(r1-1,c2)-total(r2,c1-1)+total(r1-1,c1-1))%MOD;
    while(ans<0) ans+=MOD;
    cout<<ans;
}
