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, U, V, ans;
int T;
void init() { scanf("%I64d%I64d%I64d%I64d", &L, &R, &U, &V); }
inline long long G(long long x, long long y, long long z, long long lim) {
  if (lim < x) return 0;
  long long term, sum;
  term = (y < ((lim - x) / z) + 1 ? y : ((lim - x) / z) + 1);
  sum = x + x + (term - 1) * z;
  if (term % 2 == 0)
    term /= 2;
  else
    sum /= 2;
  return ((term % MOD) * (sum % MOD)) % MOD;
}
inline long long F(long long x, long long y) {
  if (!x || !y) return 0;
  long long l = 1, r = N, mid, ret = 0, bg = 1;
  for (long long p = 0; l < r; p++) {
    mid = (l + r) >> 1;
    if (x <= mid)
      r = mid;
    else {
      ret += G(bg, mid - l + 1, 1LL << (p + 1), y), ret %= MOD;
      l = mid + 1, bg += 1LL << p;
    }
  }
  if (bg <= y) ret = (ret + bg) % MOD;
  return ret;
}
void work() {
  long long a = F(R, V), b = F(R, U - 1), c = F(L - 1, V), d = F(L - 1, U - 1);
  ans = (a - b + MOD - c + MOD + d) % MOD;
  printf("%d\n", (int)ans);
}
int main() {
  for (scanf("%I64d %d %I64d", &N, &T, &MOD); T; T--) {
    init();
    work();
  }
  return 0;
}