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:
/** In the name of Allah (SWT).
 *
 *    author:  Asif
 *    created: 00.00.2021 00:00:00
**/
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<string, string> pss;
typedef map<int, int> mii;
typedef unordered_map<int, int> umap_ii;
typedef unordered_map<string, int> umap_si;

#define FOR(i, j, k, in) for (int i = j; i < k; i += in)
#define RFOR(i, j, k, in) for (int i = j; i >= k; i -= in)
#define REP(i, j) FOR(i, 0, j, 1)
#define RREP(i, j) RFOR(i, j, 0, 1)
#define INF (int)1e9
#define PI 3.1415926535897932384626433832795
#define MOD 1000000007
#define pb push_back
#define imax INT_MAX
#define imin INT_MIN
#define VSORT sort(v.begin(), v.end())
#define VRSORT sort(v.rbegin(), v.rend())
#define V1SORT sort(v1.begin(), v1.end())
#define V1RSORT sort(v1.rbegin(), v1.rend())

/**
 * Limits in C++ for reference
 * _____________________________________________________________________________________
 * |Sr| Macro Name | Description                     | Value
 * |No|____________|_________________________________|__________________________________
 * |1.| ULLONG_MAX | Maximum value unsigned long long| 18,446,744,073,709,551,615 (10^20)
 * |2.| LLONG_MAX  | Maximum value long long         | 9,223,372,036,854,775,807 (10^19)
 * |3.| LLONG_MIN  | Minimum value long long         |-9,223,372,036,854,775,808 -1*(10^19)
 * |4.| INT_MAX    | Maximum value int               | 2,147,483,647 (10^10)
 * |5.| INT_MIN    | Minimum value int               |-2,147,483,648 (10^10)
 */

void busted()
{
    
    ll n, a, b; cin >> n >> a >> b;
    if(a == 1){
        if((n - 1) % b == 0){
            cout << "Yes\n";
        }
        else{
            cout <<"No\n";
        }
        return;
    }
    ll sum = 1;
    while(sum <= n){
        if((n - sum) % b == 0){
            cout << "Yes\n";
            return;
        }
        sum *= a;
    }
    cout << "No\n";
    return;
}

int32_t main()
{
    ll tc;
    cin >> tc;
    while (tc--)
        busted();
    return 0;
}