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: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.NoSuchElementException;

public class Main {
    private static final Mod mod = new Mod(1_000_000_007);
    private static final Mod.Combination combination =
            mod.combination(2 * 1_000_000);

    static long f(int r, int c) {
        return combination.of(r + c, r);
    }
    static long g(int r, int c) {
        Mod.Value v = mod.value(0);
        for (int i = 1; i <= r + 1; i++) {
            v.add(f(i, c));
        }
        return v.longValue();
    }
    static void solve(MyScanner in, MyWriter out) {
        int r1 = in.nextInt();
        int c1 = in.nextInt();
        int r2 = in.nextInt();
        int c2 = in.nextInt();
        Mod.Value ans = mod.value(g(r2, c2))
                           .subtract(g(r2, c1 - 1))
                           .subtract(g(r1 - 1, c2))
                           .add(g(r1 - 1, c1 - 1));
        out.println(ans);
    }
    static final class Mod {
        private final int divisor;

        Mod(int divisor) {
            if (divisor <= 0) {
                throw new IllegalArgumentException();
            }
            this.divisor = divisor;
        }
        long mod(long dividend) {
            return Math.floorMod(dividend, divisor);
        }
        long add(long a, long b) {
            return mod(mod(a) + mod(b));
        }
        long subtract(long a, long b) {
            return mod(mod(a) - mod(b));
        }
        long multiply(long a, long b) {
            return mod(mod(a) * mod(b));
        }
        long pow(long a, long b) {
            if (b < 0) {
                throw new IllegalArgumentException();
            }
            long r = 1;
            while (b > 0) {
                if ((b & 1) == 1) {
                    r = multiply(r, a);
                }
                a = multiply(a, a);
                b >>= 1;
            }
            return r;
        }
        long inverse(long a) {
            // assert isCoprime(a, divisor);
            if (a == 0) {
                throw new IllegalArgumentException();
            }
            a = mod(a);
            long b = divisor;
            long u = 1;
            long v = 0;
            while (b != 0) {
                long q = a / b;
                a -= q * b;
                u -= q * v;

                long tmp = a;
                a = b;
                b = tmp;

                tmp = u;
                u = v;
                v = tmp;
            }
            return mod(u);
        }
        long div(long a, long b) {
            return multiply(a, inverse(b));
        }
        Value value(long initialValue) {
            return new Value(this, initialValue);
        }
        Combination combination(int maxN) {
            return new Combination(divisor, maxN);
        }

        static final class Value {
            private final Mod mod;
            private long value;

            private Value(Mod mod, long initialValue) {
                this.mod = mod;
                value = mod.mod(initialValue);
            }
            long longValue() {
                return value;
            }
            Value add(long a) {
                value = mod.add(value, a);
                return this;
            }
            Value add(Value a) {
                return add(a.value);
            }
            Value subtract(long a) {
                value = mod.subtract(value, a);
                return this;
            }
            Value subtract(Value a) {
                return subtract(a.value);
            }
            Value multiply(long a) {
                value = mod.multiply(value, a);
                return this;
            }
            Value multiply(Value a) {
                return multiply(a.value);
            }
            Value pow(long a) {
                value = mod.pow(value, a);
                return this;
            }
            Value inverse() {
                value = mod.inverse(value);
                return this;
            }
            Value div(long a) {
                value = mod.div(value, a);
                return this;
            }
            Value div(Value a) {
                return div(a.value);
            }
            @Override
            public String toString() {
                return Long.toString(value);
            }
        }
        // https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
        // http://drken1215.hatenablog.com/entry/2018/06/08/210000
        static final class Combination {
            private final int divisor;
            private final long[] factorial;
            private final long[] factorialInverse;

            private Combination(int divisor, int maxN) {
                this.divisor = divisor;
                factorial = new long[maxN + 1];
                long[] inverse = new long[factorial.length];
                factorialInverse = new long[factorial.length];

                factorial[0] = factorial[1] = 1;
                inverse[1] = 1;
                factorialInverse[0] = factorialInverse[1] = 1;
                for (int i = 2; i < factorial.length; i++) {
                    factorial[i] = factorial[i - 1] * i % divisor;
                    inverse[i] = divisor
                                 - inverse[divisor % i]
                                   * (divisor / i)
                                   % divisor;
                    factorialInverse[i] =
                            factorialInverse[i - 1] * inverse[i] % divisor;
                }
            }
            long of(int n, int k) {
                if (k > n) {
                    return 0;
                }
                return factorial[n]
                       * (factorialInverse[k]
                          * factorialInverse[n - k]
                          % divisor)
                       % divisor;
            }
        }
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this.in = in;
        }
        private byte readByte() {
            if (point < readLength) {
                byte result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(byte c) {
            return 33 <= c && c <= 126;
        }
        public char nextChar() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        public String next() {
            return next(16);
        }
        public String next(int n) {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        public long nextLong() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        public int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        public long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        public char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        public char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        public int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        public long[][] nextVerticalLongArrays(int arrayCount,
                                               int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        public char[][] nextVerticalCharArrays(int arrayCount,
                                               int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        public void joinAndPrintln(int[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(int[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(long[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(long[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(Iterable<?> iterable) {
            joinAndPrintln(iterable, " ");
        }
        public void joinAndPrintln(Iterable<?> iterable, String delimiter) {
            StringBuilder b = new StringBuilder();
            for (Iterator<?> i = iterable.iterator(); i.hasNext();) {
                b.append(i.next());
                while (i.hasNext()) {
                    b.append(delimiter).append(i.next());
                }
            }
            println(b.toString());
        }
    }
}