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, M, MOD;
pair<long long, long long> Q(long long n, long long imax, long long vmax) {
  if (vmax == 0) return make_pair(0, 0);
  if (imax == 0) return make_pair(0, 0);
  if (imax == 1) return make_pair(1, 1);
  if (n == 1) return make_pair(1, 1);
  if (n == 0) return make_pair(0, 0);
  long long mid = (n + 1) / 2;
  if (imax > mid) {
    pair<long long, long long> para;
    para = Q(n - mid, imax - mid, vmax / 2);
    return make_pair(((min(((vmax + 1) / 2), mid) % MOD) *
                          (min(((vmax + 1) / 2), mid) % MOD) % MOD +
                      2 * para.first % MOD) %
                         MOD,
                     (min(((vmax + 1) / 2), mid) % MOD) + para.second);
  } else {
    pair<long long, long long> para;
    para = Q(mid, imax, (vmax + 1) / 2);
    return make_pair((2 * para.first - para.second) % MOD, para.second % MOD);
  }
}
long long querry(long long l, long long r, long long u, long long v) {
  return ((Q(N, r, v).first - Q(N, r, u - 1).first - Q(N, l - 1, v).first +
           Q(N, l - 1, u - 1).first) %
              MOD +
          MOD) %
         MOD;
}
int main() {
  long long l, r, u, v;
  cin >> N >> M >> MOD;
  for (int i = 1; i <= M; ++i) {
    cin >> l >> r >> u >> v;
    cout << querry(l, r, u, v) << '\n';
  }
  return 0;
}