Problem: There is an infinite set generated as follows:

  * 1 is in this set. 
  * If x is in this set, x ⋅ a and x+b both are in this set. 



For example, when a=3 and b=6, the five smallest elements of the set are:

  * 1, 
  * 3 (1 is in this set, so 1⋅ a=3 is in this set), 
  * 7 (1 is in this set, so 1+b=7 is in this set), 
  * 9 (3 is in this set, so 3⋅ a=9 is in this set), 
  * 13 (7 is in this set, so 7+b=13 is in this set). 



Given positive integers a, b, n, determine if n is in this set.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 10^5) — the number of test cases. The description of the test cases follows.

The only line describing each test case contains three integers n, a, b (1≤ n,a,b≤ 10^9) separated by a single space.

Output

For each test case, print "Yes" if n is in this set, and "No" otherwise. You can print each letter in any case.

Example

Input


5
24 3 5
10 3 6
2345 1 4
19260817 394 485
19260817 233 264


Output


Yes
No
Yes
No
Yes

Note

In the first test case, 24 is generated as follows:

  * 1 is in this set, so 3 and 6 are in this set; 
  * 3 is in this set, so 9 and 8 are in this set; 
  * 8 is in this set, so 24 and 13 are in this set. 



Thus we can see 24 is in this set.

The five smallest elements of the set in the second test case is described in statements. We can see that 10 isn't among them.

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
using namespace chrono;

#define fastio() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define endl '\n'
#define MOD 1000000007
#define MOD1 998244353
#define INF 1e18
#define PI 3.141592653589793238462
#define set_bits __builtin_popcountll
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()

typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
/*----------------------------------------------------------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------------------------------------------------------*/

// bool check(ll n, ll a, ll b, ll c)
// {
// 	if (min((c * a), (b + c)) > n)
// 		return false;
// 	if ((log(c * a) == log(n)) || (n % (b + c) == 0))
// 	{
// 		return true;
// 	}

// }

void solve()
{
	ll n, a, b;
	cin >> n >> a >> b;
	ll flag = 1;
	if (a == 1)
	{
		if ((n - 1) % b == 0)
			cout << "YES" << endl;
		else
			cout << "NO" << endl;
		return;
	}

	while (flag <= n)
	{
		ll j = (n - flag);
		if (j % b == 0)
		{
			cout << "YES" << endl;
			return;
		}
		flag = flag * a;
	}

	cout << "NO" << endl;
}

int main()
{
#ifndef ONLINE_JUDGE
	freopen("Input.txt", "r", stdin);
	freopen("Output.txt", "w", stdout);
	freopen("Error.txt", "w", stderr);
#endif
	fastio();
	auto start1 = high_resolution_clock::now();
	int t = 1;
	cin >> t;
	while (t--)
	{
		solve();
	}
	auto stop1 = high_resolution_clock::now();
	auto duration = duration_cast<microseconds>(stop1 - start1);
#ifndef ONLINE_JUDGE
	cerr << "Time: " << duration . count() / 1000 << endl;
#endif
	return 0;
}