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, l_, r_, m;
long long u, v;
void read(long long &x) {
  char ch;
  while (ch = getchar(), ch < '0')
    ;
  x = ch - '0';
  while (ch = getchar(), ch >= '0') x = x * 10 + ch - '0';
}
long long Get(long long st, long long ed, long long d) {
  if ((st + ed) & 1)
    return ((st + ed) % mod) * (((ed - st) / d + 1) / 2 % mod) % mod;
  return (st + ed) / 2 % mod * (((ed - st) / d + 1) % mod) % mod;
}
long long ans(long long st, long long d, long long n, long long l,
              long long r) {
  if (n == 1)
    if (st >= v && st <= u)
      return st;
    else
      return 0;
  if (st + (n - 1) * d < v || st > u) return 0;
  if (l == 1 && r == n)
    return Get(max(((v - st - 1 + d) / d) * d + st, st),
               min(((u - st) / d) * d + st, st + (n - 1) * d), d);
  if (r <= (n + 1) / 2) return ans(st, d * 2, (n + 1) / 2, l, r);
  if (l > (n + 1) / 2)
    return ans(st + d, d * 2, n / 2, l - (n + 1) / 2, r - (n + 1) / 2);
  return (ans(st, d * 2, (n + 1) / 2, l, (n + 1) / 2) +
          ans(st + d, d * 2, n / 2, 1, r - (n + 1) / 2)) %
         mod;
}
int main() {
  read(n_);
  read(m);
  read(mod);
  for (; m--;) {
    read(l_);
    read(r_);
    read(v);
    read(u);
    printf("%d\n", (int)ans(1, 1, n_, l_, r_));
  }
  return 0;
}