#include <bits/stdc++.h>
using namespace std;
template <typename Number>
Number gcd(Number m, Number n) {
  if (m < n) swap(m, n);
  if (n == 0) return m;
  return gcd(m % n, n);
}
long long int binSearch(vector<long long int> v, long long int l,
                        long long int r, long long int x) {
  if (r >= l) {
    long long int mid = l + (r - l) / 2;
    if (v[mid] == x) return mid;
    if (v[mid] > x) return binSearch(v, l, mid - 1, x);
    return binSearch(v, mid + 1, r, x);
  }
  return -1;
}
long long int power(long long int a, long long int b) {
  long long int result = 1;
  while (b > 0) {
    if (b % 2 == 1) result *= a;
    a *= a;
    b /= 2;
  }
  return result;
}
void solve() {
  long long int m, d, w;
  cin >> m >> d >> w;
  long long int tp = gcd(d - 1, w);
  w = w / tp;
  long long int cnt = min(d, m) / w;
  cout << ((2 * (min(m, d) - w) - w * (cnt - 1)) * cnt / 2) << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t;
  t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

Berland year consists of m months with d days each. Months are numbered from 1 to m. Berland week consists of w days. The first day of the year is also the first day of the week. Note that the last week of the year might be shorter than w days.

A pair (x, y) such that x < y is ambiguous if day x of month y is the same day of the week as day y of month x.

Count the number of ambiguous pairs.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

Each of the next t lines contains three integers m, d and w (1 ≤ m, d, w ≤ 10^9) — the number of months in a year, the number of days in a month and the number of days in a week.

Output

Print t integers — for each testcase output the number of pairs (x, y) such that x < y and day x of month y is the same day of the week as day y of month x.

Example

Input


5
6 7 4
10 7 12
12 30 7
1 1 1
3247834 10298779 625324


Output


6
9
5
0
116461800

Note

Here are the pairs for the first test case: 

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename Number>
Number gcd(Number m, Number n) {
  if (m < n) swap(m, n);
  if (n == 0) return m;
  return gcd(m % n, n);
}
long long int binSearch(vector<long long int> v, long long int l,
                        long long int r, long long int x) {
  if (r >= l) {
    long long int mid = l + (r - l) / 2;
    if (v[mid] == x) return mid;
    if (v[mid] > x) return binSearch(v, l, mid - 1, x);
    return binSearch(v, mid + 1, r, x);
  }
  return -1;
}
long long int power(long long int a, long long int b) {
  long long int result = 1;
  while (b > 0) {
    if (b % 2 == 1) result *= a;
    a *= a;
    b /= 2;
  }
  return result;
}
void solve() {
  long long int m, d, w;
  cin >> m >> d >> w;
  long long int tp = gcd(d - 1, w);
  w = w / tp;
  long long int cnt = min(d, m) / w;
  cout << ((2 * (min(m, d) - w) - w * (cnt - 1)) * cnt / 2) << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t;
  t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

```