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;
long long mod=1000000007;
long long mypow(long a,long long b) {
  long long c;
  if (b==0) return 1;
  else {
    c=mypow(a,b/2)*mypow(a,b/2)%mod;
    if (b%2==1) c=c*a%mod;
    return c;
  }
}
vector<long long> fac(2000003);
vector<long long> minv(2000003);
void myfact(long n) {
  long i;
  fac.at(0)=1;
  minv.at(0)=1;
  for(i=1;i<=n;i++) {
    fac.at(i)=i*fac.at(i-1)%mod;
    minv.at(i)=mypow(fac.at(i),mod-2)%mod;
  }
}
long long mycomb(long n,long r) {
  long long c;
  c=fac.at(n)*minv.at(r)%mod*minv.at(n-r)%mod;
  return c;
}
int main() {
  long r1,c1,r2,c2;
  long long a;
  cin>>r1>>c1>>r2>>c2;
  myfact(r2+c2+2);
  a=(mycomb(r2+c2+2,r2+1)-mycomb(r2+c1+1,r2+1)-mycomb(r1+c2+1,r1)+mycomb(r1+c1,r1))%mod;
  if (a<0) a+=mod;
  cout<<a<<endl;
}
//1≤r1≤r2≤10^6
//1≤c1≤c2≤10^6