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 MOD;
inline long long mod(long long x) { return x % MOD + (MOD * (x % MOD < 0)); }
long long cal(long long d, long long r, long long m) {
  long long k = (m - r) / d;
  if (m < r) return 0;
  return mod(mod(r) * mod(k + 1) + mod(d) * mod(mod(k) * mod(k + 1) / 2));
}
long long qry(long long k, long long m, long long d, long long r, long long l) {
  long long p = l / 2 + (l % 2);
  if (k == 0 or m == 0) return 0;
  if (l == 1) return mod((r + d * (r == 0)) * ((r + d * (r == 0)) <= m));
  if (k <= p) {
    return mod(qry(k, m, d * 2, r + d * (r == 0), p));
  } else {
    return mod(qry(k - p, m, d * 2, r + (d * (r != 0)), l - p) +
               cal(d * 2, r + d * (r == 0), m));
  }
}
int main() {
  long long n, m;
  long long i;
  long long a, b, c, d;
  cin >> n >> m >> MOD;
  for (i = 0; i < m; i++) {
    cin >> a >> b >> c >> d, d = min(d, n);
    if (c > n) {
      printf("0\n");
      continue;
    }
    cout << mod(mod(qry(b, d, 1, 0, n) - qry(b, c - 1, 1, 0, n)) -
                mod(qry(a - 1, d, 1, 0, n) - qry(a - 1, c - 1, 1, 0, n)))
         << endl;
  }
  return 0;
}