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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        F solver = new F();
        solver.solve(1, in, out);
        out.close();
    }

    static class F {
        static long MOD = (long) (1e9 + 7);
        private static int MAX = 3000000;
        private static long[] xs = new long[MAX + 1];
        private static long[] ys = new long[MAX + 1];

        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int r1 = in.nextInt();
            int c1 = in.nextInt();
            int r2 = in.nextInt();
            int c2 = in.nextInt();

            r1--;
            c1--;
            long ans = comb(r2 + c2 + 2, r2 + 1);
            ans -= comb(r1 + c2 + 2, r1 + 1);
            ans -= comb(r2 + c1 + 2, r2 + 1);
            ans += comb(r1 + c1 + 2, r1 + 1);
            out.println(ans % MOD);
        }

        private long comb(int n, int r) {
            if (r < 0 || r > n) return 0;
            long key = (long) (n * 1e7 + r);
            if (xs[0] == 0) {
                xs[0] = 1;
                for (int i = 1; i <= MAX; i++) {
                    xs[i] = xs[i - 1] * i % MOD;
                }
                long inv = modpow(xs[MAX]);
                ys[MAX] = inv;
                for (int i = MAX; i >= 1; i--) {
                    inv = inv * i % MOD;
                    ys[i - 1] = inv;
                }
            }
            return xs[n] * (ys[r] * ys[n - r] % MOD) % MOD;
        }

        private long modpow(long a) {
            return modpow(a, MOD - 2);
        }

        private long modpow(long a, long n) {
            long r = 1;
            while (n > 0) {
                r = r * ((n % 2) != 0 ? a : 1) % MOD;
                a = a * a % MOD;
                n >>= 1;
            }
            return r;
        }

    }

    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}