Problem: Let a be an array consisting of n numbers. The array's elements are numbered from 1 to n, even is an array consisting of the numerals whose numbers are even in a (eveni = a2i, 1 ≤ 2i ≤ n), odd is an array consisting of the numberals whose numbers are odd in а (oddi = a2i - 1, 1 ≤ 2i - 1 ≤ n). Then let's define the transformation of array F(a) in the following manner:

  * if n > 1, F(a) = F(odd) + F(even), where operation " + " stands for the arrays' concatenation (joining together) 
  * if n = 1, F(a) = a



Let a be an array consisting of n numbers 1, 2, 3, ..., n. Then b is the result of applying the transformation to the array a (so b = F(a)). You are given m queries (l, r, u, v). Your task is to find for each query the sum of numbers bi, such that l ≤ i ≤ r and u ≤ bi ≤ v. You should print the query results modulo mod.

Input

The first line contains three integers n, m, mod (1 ≤ n ≤ 1018, 1 ≤ m ≤ 105, 1 ≤ mod ≤ 109). Next m lines describe the queries. Each query is defined by four integers l, r, u, v (1 ≤ l ≤ r ≤ n, 1 ≤ u ≤ v ≤ 1018).

Please do not use the %lld specificator to read or write 64-bit integers in C++. Use %I64d specificator.

Output

Print m lines each containing an integer — remainder modulo mod of the query result.

Examples

Input

4 5 10000
2 3 4 5
2 4 1 3
1 2 2 4
2 3 3 5
1 3 3 4


Output

0
5
3
3
3


Input

2 5 10000
1 2 2 2
1 1 4 5
1 1 2 5
1 1 1 3
1 2 5 5


Output

2
0
0
1
0

Note

Let's consider the first example. First let's construct an array b = F(a) = F([1, 2, 3, 4]). 

  * Step 1. F([1, 2, 3, 4]) = F([1, 3]) + F([2, 4])
  * Step 2. F([1, 3]) = F([1]) + F([3]) = [1] + [3] = [1, 3]
  * Step 3. F([2, 4]) = F([2]) + F([4]) = [2] + [4] = [2, 4]
  * Step 4. b = F([1, 2, 3, 4]) = F([1, 3]) + F([2, 4]) = [1, 3] + [2, 4] = [1, 3, 2, 4]

Thus b = [1, 3, 2, 4]. Let's consider the first query l = 2, r = 3, u = 4, v = 5. The second and third positions in the array b do not have numbers in the range [4, 5], so the sum obviously equals zero. Let's consider the second query l = 2, r = 4, u = 1, v = 3. The second and third positions have two numbers that belong to the range [1, 3], their sum equals 5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long n;
int m, mod;
pair<int, long long> fnd(long long n, long long l, long long r, long long u,
                         long long v) {
  l = max(l, (long long)0);
  r = min(n - 1, r);
  u = max(u, (long long)1);
  v = min(n, v);
  if (l > r || u > v) return make_pair(0, 0);
  pair<int, long long> res;
  if (l == 0 && r == n - 1) {
    long long a, b;
    a = u + v;
    b = v - u + 1;
    if (a % 2 == 0)
      a /= 2;
    else
      b /= 2;
    res = make_pair(a % mod * (b % mod) % mod, v - u + 1);
    return res;
  }
  pair<int, long long> r1, r2;
  r1 = fnd((n + 1) / 2, l, r, u / 2 + 1, (v + 1) / 2);
  r2 = fnd(n / 2, l - (n + 1) / 2, r - (n + 1) / 2, (u + 1) / 2, v / 2);
  int a, b;
  a = ((2 * r1.first - r1.second % mod) % mod + mod) % mod;
  b = 2 * r2.first % mod;
  res = make_pair((a + b) % mod, r1.second + r2.second);
  return res;
}
int main() {
  int i, j, k;
  for (; cin >> n >> m >> mod;) {
    for (k = 0; k < m; ++k) {
      long long l, r, u, v;
      cin >> l >> r >> u >> v;
      --l;
      --r;
      int res = fnd(n, l, r, u, v).first;
      printf("%d\n", res);
    }
  }
  return 0;
}