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: Runtime Error)

#include <bits/stdc++.h>
 
using namespace std;

#define M 1000000007
#define pb emplace_back
#define f first
#define s second
#define rep(i, st, ed) for(ll i=st; i<ed; ++i)
#define repn(i, st, ed) for(ll i=st; i<=ed; ++i)
#define repb(i, ed, st) for(ll i=ed; i>=st; --i)
#define all(v) v.begin(),v.end()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define PI acosl(-1.0)
#define mp(a, b) make_pair(a, b)
#define eps 1e-9

typedef long long ll;
typedef unsigned long long int llt;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef vector<ll> vec;
typedef vector<pll> vecp;
typedef map<ll, ll> mpll;


const int N = 1e5 + 10;
const ll INF = 1LL << 60;

template<class T> void chmax(T &a,T b) { if (a<b) a=b;}
template<class T> void chmin(T &a,T b) { if (a>b) a=b;}

template <typename A, typename B>
string to_string(pair<A, B> p);
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
 
string to_string(const string& s) {
  return '"' + s + '"';
}
 
string to_string(const char* s) {
  return to_string((string) s);
}
 
string to_string(bool b) {
  return (b ? "true" : "false");
}
 
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
 
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
 
void debug_out() { cerr << endl; }
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << to_string(H) << endl;
  debug_out(T...);
}
#define LOCAL 3
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:" << endl, debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
ll ppow(ll x, ll y, ll mod)
{
  ll res = 1;
  while(y > 0){
    if(y&1)
      res = (res * x)%mod;
    y = y >> 1;
    x = (x * x)%mod;
  }
  return res;
}
ll factdp[N];
ll invfact[N];
ll fact(ll x)
{
  if(x == 0) return 1;
  if(x == 1) return 1;
  if(factdp[x] != 0) return factdp[x];
  return factdp[x] = (x*fact(x-1))%M;
}
// Combination
ll inv(ll x)
{
  if(invfact[x] != 0) return invfact[x];
  return invfact[x] = ppow(x, M-2, M);
}
ll modcomb(ll n, ll r)
{
  if(n < r) return 0;
  ll res = fact(n);
  (res *= inv(fact(r))) %= M;
  (res *= inv(fact(n-r))) %= M;
  return res;
}
void solve()
{
    ll r1, c1, r2, c2;
    cin>>r1>>c1>>r2>>c2;
    ll ans = 0;
    repn(i, c1, c2){
    	ll tans = modcomb(i+r2+1, i+1) - modcomb(i+r1, i+1);
    	ans = (ans + tans) % M;
    }
    cout<<ans<<endl;
}


int main()
{
    ll Tests = 1;
    //cin>>Tests;
    while(Tests--)
    {
        solve();
    }
    return 0;
}