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 <algorithm>
#include <array>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <valarray>
#include <vector>

#include <cassert>
#include <cctype>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include <chrono>
#include <random>
#include <thread>
#include <unordered_map>
#include <unordered_set>

using namespace std;

#define all(c) c.begin(), c.end()
#define repeat(i, n) for (int i = 0; i < static_cast<int>(n); i++)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define dump(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define dump(x)
#endif

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "{";
    for (auto it = v.begin(); it != v.end(); ++it) {
        if (it != v.begin())
            os << ",";
        os << *it;
    }
    return os << "}";
}

template <typename A, typename B>
ostream& operator<<(ostream& os, const pair<A, B>& v)
{
    os << "{";
    os << v.first << ", " << v.second;
    return os << "}";
}

// ---------------------------------------------------------------------------

using point = complex<double>;
using ll = long long;

const ll MOD = 1000000007;
template <typename T, typename F>
T apply_doubling(const T& x,
    const long long& n,
    const T& id_elem,
    const F& binary_op)
{
    if (n == 0)
        return id_elem;
    T ret = apply_doubling(binary_op(x, x), n / 2, id_elem, binary_op);
    if (n % 2 == 1)
        ret = binary_op(ret, x);
    return ret;
}

long long mod_pow(long long x, long long n, long long mod)
{
    return apply_doubling(x, n, 1ll, [mod](ll a, ll b) { return a * b % mod; });
}

long long mod_inv(long long x, long long mod)
{
    return mod_pow(x, mod - 2, mod);
}

const int MAXIN = 1000010;
ll fact[MAXIN] = { 0 };

int my_main(int argc, char** argv)
{
    ios::sync_with_stdio(false);
    cin.tie(0);

    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;


    fact[0] = 1;
    for (int i = 1; i < MAXIN; i++)
        fact[i] = i * fact[i - 1] % MOD;

    auto combi = [](ll n, ll k) -> ll {
        ll ret = 1;
        ret = ret * fact[n] % MOD;
        ret = ret * mod_inv(fact[n - k], MOD) % MOD;
        ret = ret * mod_inv(fact[k], MOD) % MOD;

        return ret;
    };

    auto g = [&](int r, int c) {
        ll ret = 0;
        for (int i = 1; i <= r + 1; i++) {
            ret += combi(c + i, i);
            ret %= MOD;
        }
        return ret;
    };

    ll ret = g(r2, c2);
    ret -= g(r2, c1 - 1);
    ret = (ret + MOD) % MOD;
    ret -= g(r1 - 1, c2);
    ret = (ret + MOD) % MOD;

    ret += g(r1 - 1, c1 - 1);
    ret %= MOD;

    cout << ret << endl;
    return 0;
}

// ----------------------------------------------------------------------------
// Test driver

#ifdef DEBUG
#define MAY_RUN_TESTCASE
#endif

#ifdef MAY_RUN_TESTCASE
#include <fstream>

#if __has_include(<unistd.h>)
// Mac, Linux
#include <unistd.h>
#elif __has_include(<io.h>)
// Windows
#include <io.h>
#else
// Other?
#error "unistd.h or io.h not found"
#endif

bool test_file_exists(const std::string& str)
{
    std::ifstream fs(str);
    return fs.is_open();
}

#endif

int main(int argc, char** argv)
{
#ifndef MAY_RUN_TESTCASE
    return my_main(argc, argv);
#else
    if (argc == 1) {
        return my_main(argc, argv);
    } else if (argc == 2) {

        char* stdin_file = argv[1];
        freopen(stdin_file, "r", stdin);
        return my_main(argc, argv);

    } else if (argc == 5) {

        std::string stdin_file = argv[1];
        std::string expected_file = argv[2];
        std::string stdout_file = argv[3];
        std::string stderr_file = argv[4];

        if (!test_file_exists(stdin_file)) {
            std::cerr << stdin_file << " not found" << std::endl;
            return 3;
        }

        if (!test_file_exists(expected_file)) {
            std::cerr << expected_file << " not found" << std::endl;
            return 3;
        }

        int original_stdin = dup(fileno(stdin));
        int original_stdout = dup(fileno(stdout));
        int original_stderr = dup(fileno(stderr));

        freopen(stdin_file.c_str(), "r", stdin);
        freopen(stdout_file.c_str(), "w", stdout);
        freopen(stderr_file.c_str(), "w", stderr);

        int ret = my_main(argc, argv);

        fflush(stdout);
        fflush(stderr);

        dup2(original_stderr, fileno(stderr));
        dup2(original_stdout, fileno(stdout));
        dup2(original_stdin, fileno(stdin));

        if (ret != 0) {
            std::cerr << "main returns " << ret << std::endl;
            return ret;
        }

        std::ifstream inp(stdin_file);
        std::ifstream out(stdout_file);
        std::ifstream err(stderr_file);
        std::ifstream exp(expected_file);

        // Clear is needed if the file is empty.
        std::cout << "----- input -----" << std::endl;
        std::cout << inp.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "----- output ----" << std::endl;
        std::cout << out.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "---- expected ---" << std::endl;
        std::cout << exp.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl
                  << std::endl;

        std::cout << "----- stderr ----" << std::endl;
        std::cout << err.rdbuf() << std::endl;
        std::cout.clear();
        std::cout << "-----------------" << std::endl;

        inp.seekg(0);
        out.seekg(0);
        exp.seekg(0);
        err.seekg(0);

        std::string output_str, expected_str;
        {
            std::stringstream output_ss;
            output_ss << out.rdbuf();
            output_str = output_ss.str();

            std::stringstream expected_ss;
            expected_ss << exp.rdbuf();
            expected_str = expected_ss.str();
        }

        // Remove trailing spaces
        output_str.erase(output_str.find_last_not_of(" \n\r\t") + 1);
        expected_str.erase(expected_str.find_last_not_of(" \n\r\t") + 1);

        if (output_str == expected_str)
            return 0;
        else
            return 1;
    }
    return 1;
#endif
}