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, mod;
long long get(long long l, long long r, long long u, long long v,
              long long le = 0, long long ri = n, long long pot = 1,
              long long cte = 0) {
  if (l > r) return 0;
  if (l == le && r == ri) {
    if (v < cte) return 0;
    long long mini = 0, maxi = (n - cte) / pot;
    u = max(u, cte);
    mini = max(mini, (u - cte + pot - 1) / pot);
    maxi = min(maxi, (v - cte) / pot);
    if (mini > maxi) return 0;
    long long mod2 = mod * 2;
    long long A = (maxi % mod2) * ((maxi + 1) % mod2) % mod2;
    long long B = (mini % mod2) * ((mini - 1 + mod2) % mod2) % mod2;
    long long C = (A - B + mod2) % mod2;
    C = C / 2;
    C = C * (pot % mod) % mod;
    C = (C + ((cte + 1) % mod) * ((maxi - mini + 1) % mod)) % mod;
    return C;
  } else {
    long long mid = (le + ri) / 2;
    long long ret =
        get(l, min(r, mid), u, v, le, mid, pot * 2, cte) +
        get(max(l, mid + 1), r, u, v, mid + 1, ri, pot * 2, cte + pot);
    if (ret >= mod) ret -= mod;
    return ret;
  }
}
int main() {
  int m;
  cin >> n >> m >> mod;
  n--;
  while (m--) {
    long long l, r, u, v;
    scanf("%I64d %I64d %I64d %I64d", &l, &r, &u, &v);
    u--;
    v--;
    l--;
    r--;
    printf("%I64d\n", get(l, r, u, v));
  }
}