Problem:
Score : 600 points

Problem Statement

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using vb=vector<bool>;
using vvb=vector<vb>;
using vd=vector<double>;
using vvd=vector<vd>;
using vi=vector<int>;
using vvi=vector<vi>;
using vl=vector<ll>;
using vvl=vector<vl>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll>;
using tlll=tuple<ll,ll,ll>;
using vs=vector<string>;

#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define rep(i,n) range(i,0,n)
#define rrep(i,n) for(ll i=(n)-1;i>=0;i--)
#define range(i,a,n) for(ll i=(a);i<(n);i++)

#define LINF ((ll)1ll<<60)
#define INF ((int)1<<30)
#define EPS (1e-9)
#define MOD (1000000007ll)
#define fcout(a) cout<<setprecision(a)<<fixed
#define fs first
#define sc second
#define PI 3.1415926535897932384

int dx[]={1,0,-1,0,1,-1,-1,1},dy[]={0,1,0,-1,1,1,-1,-1};

template<class T>bool chmax(T&a,T b){if(a<b){a=b; return true;}return false;}
template<class T>bool chmin(T&a,T b){if(a>b){a=b; return true;}return false;}
template<class S>S acm(vector<S>&a){return accumulate(all(a),S());}
template<class S>S max(vector<S>&a){return *max_element(all(a));}
template<class S>S min(vector<S>&a){return *min_element(all(a));}
void YN(bool b){cout<<(b?"YES":"NO")<<"\n";}
void Yn(bool b){cout<<(b?"Yes":"No")<<"\n";}
void yn(bool b){cout<<(b?"yes":"no")<<"\n";}
int sgn(const double&r){return (r>EPS)-(r<-EPS);} // a>0  : sgn(a)>0
int sgn(const double&a,const double&b){return sgn(a-b);} // b<=c : sgn(b,c)<=0

ll max(int a,ll b){return max((ll)a,b);} ll max(ll a,int b){return max(a,(ll)b);}
template<class T>void puta(T&&t){cout<<t<<"\n";}
template<class H,class...T>void puta(H&&h,T&&...t){cout<<h<<' ';puta(t...);}
template<class S,class T>ostream&operator<<(ostream&os,pair<S,T>p){os<<"["<<p.first<<", "<<p.second<<"]";return os;};
template<class S>auto&operator<<(ostream&os,vector<S>t){bool a=1; for(auto s:t){os<<(a?"":" ")<<s;a=0;} return os;}

vl fact,finv;
ll modpw(ll x,ll k){
	ll res=1;
	while(k!=0){
		if(k&1)res=res*x%MOD;
		x=x*x%MOD;
		k=k>>1;
	}
	return res;
}

ll comb(ll n,ll k) {
	if(n==0&&k==0)return 1;
	if(n<k||n<0)return 0;
	return fact[n]*finv[n-k]%MOD*finv[k]%MOD;
}

struct ferm{
	ferm(ll n){
		fact.resize(n);
		finv.resize(n);
		fact[0]=1;
		finv[0]=1;
		rep(i,n-1){
			fact[i+1]=(fact[i]*(i+1))%MOD;
			finv[i+1]=modpw(fact[i+1],MOD-2);
		}
	}
};

ll f(ll r,ll c){
	ll ret=0;
	if(r<c)swap(r,c);
	range(i,1,r+2){
		ret+=comb(c+i,c);
		ret%=MOD;
	}
	return ret;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	ferm(2000010);
	ll r1,r2,c1,c2;
	cin>>r1>>c1>>r2>>c2;
	ll ans=f(r2,c2)-f(r2,c1-1)-f(r1-1,c2)+f(r1-1,c1-1);
	ans+=5*MOD;
	ans%=MOD;
	cout<<ans<<endl;
}