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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.stream.Collectors;

public class Main {
    static int mod = (int) (1e9) + 7;

    /* ======================DSU===================== */
    static class dsu {
        static int parent[], n;// min[],value[];
        static long size[];

        dsu(int n) {
            parent = new int[n + 1];
            size = new long[n + 1];
            // min=new int[n+1];
            // value=new int[n+1];
            this.n = n;
            makeSet();
        }

        static void makeSet() {
            for (int i = 1; i <= n; i++) {
                parent[i] = i;
                size[i] = 1;
                // min[i]=i;
            }
        }

        static int find(int a) {
            if (parent[a] == a)
                return a;
            else {
                return parent[a] = find(parent[a]);// Path Compression
            }
        }

        static void union(int a, int b) {
            int setA = find(a);
            int setB = find(b);
            if (setA == setB)
                return;
            if (size[setA] >= size[setB]) {
                parent[setB] = setA;
                size[setA] += size[setB];
            } else {
                parent[setA] = setB;
                size[setB] += size[setA];
            }
        }
    }

    /* ======================================================== */
    static class Pair<X extends Number, Y extends Number> implements Comparator<Pair> {
        X x;
        Y y;

        // Constructor
        public Pair(X x, Y y) {
            this.x = x;
            this.y = y;
        }

        public Pair() {

        }

        @Override
        public int compare(Main.Pair o1, Main.Pair o2) {
            return ((int) (o1.y.intValue() - o2.y.intValue()));// Ascending Order based on 'y'
        }
    }

    /* ===============================Tries================================= */
    static class TrieNode {
        private HashMap<Character, TrieNode> children = new HashMap<>();
        public int size;
        boolean endOfWord;

        public void putChildIfAbsent(char ch) {
            children.putIfAbsent(ch, new TrieNode());
        }

        public TrieNode getChild(char ch) {
            return children.get(ch);
        }
    }

    static private TrieNode root;

    public static void insert(String str) {
        TrieNode curr = root;
        for (char ch : str.toCharArray()) {
            curr.putChildIfAbsent(ch);
            curr = curr.getChild(ch);
            curr.size++;
        }
        // mark the current nodes endOfWord as true
        curr.endOfWord = true;
    }

    public static int search(String word) {
        TrieNode curr = root;

        for (char ch : word.toCharArray()) {
            curr = curr.getChild(ch);
            if (curr == null) {
                return 0;
            }
        }
        // size contains words starting with prefix- word
        return curr.size;
    }

    public boolean delete(TrieNode current, String word, int index) {
        if (index == word.length()) {
            // when end of word is reached only delete if currrent.endOfWord is true.
            if (!current.endOfWord) {
                return false;
            }
            current.endOfWord = false;
            // if current has no other mapping then return true
            return current.children.size() == 0;
        }
        char ch = word.charAt(index);
        TrieNode node = current.children.get(ch);
        if (node == null) {
            return false;
        }
        boolean shouldDeleteCurrentNode = delete(node, word, index + 1);

        // if true is returned then delete the mapping of character and trienode
        // reference from map.
        if (shouldDeleteCurrentNode) {
            current.children.remove(ch);
            // return true if no mappings are left in the map.
            return current.children.size() == 0;
        }
        return false;
    }

    /* ================================================================= */
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] intArr(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] longArr(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

    static FastReader f = new FastReader();
    static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (long i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static int lowerBound(int a[], int x) { // x is the target, returns lowerBound. If not found return -1
        int l = -1, r = a.length, flag = 0;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (x == a[m])
                flag = 1;
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    static int upperBound(int a[], int x, int l, int r) {// x is the target, returns upperBound. If not found return -1
        int flag = 0;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] == x)
                return m;
            if (a[m] <= x) {
                l = m;
                flag = 1;
            } else
                r = m;
        }
        return l + 1;
    }

    static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long power(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x);
            y >>= 1;
            x = (x * x);
        }
        return res;
    }

    public double binPow(double x, int n) {// binary exponentiation with negative power as well
        if (n == 0)
            return 1.0;
        double binPow = binPow(x, n / 2);
        if (n % 2 == 0) {
            return binPow * binPow;
        } else {
            return n > 0 ? (binPow * binPow * x) : (binPow * binPow / x);
        }
    }

    static long ceil(long x, long y) {
        return (x % y == 0 ? x / y : (x / y + 1));
    }

    /*
     * ===========Modular Operations==================
     */
    static long modPower(long x, long y, long p) {
        long res = 1;
        x = x % p;
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; // y = y/2
            x = (x * x) % p;
        }
        return res;
    }

    static long modInverse(long n, long p) {
        return modPower(n, p - 2, p);
    }

    static long modAdd(long a, long b) {
        return ((a + b + mod) % mod);
    }

    static long modMul(long a, long b) {
        return ((a % mod) * (b % mod)) % mod;
    }

    static long nCrModPFermat(int n, int r) {
        if (r == 0)
            return 1;
        long[] fac = new long[n + 1];
        fac[0] = 1;
        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i % mod;
        return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod) % mod) % mod;
    }

    /*
     * ===============================================
     */

    static void ruffleSort(long[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            long temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        Random r = new Random();
        for (int i = 0; i < a.length; i++) {
            int oi = r.nextInt(n);
            int temp = a[i];
            a[i] = a[oi];
            a[oi] = temp;
        }
        Arrays.sort(a);
    }

    static String binString32(int n) {
        StringBuilder str = new StringBuilder("");
        String bin = Integer.toBinaryString(n);
        if (bin.length() != 32) {
            for (int k = 0; k < 32 - bin.length(); k++) {
                str.append("0");
            }
            str.append(bin);
        }
        return str.toString();
    }

    static class sparseTable {
        public static int st[][];
        public static int log = 4;

        static int func(int a, int b) {// make func as per question(here min range query)
            return (int) gcd(a, b);
        }

        void makeTable(int n, int a[]) {

            st = new int[n][log];
            for (int i = 0; i < n; i++) {
                st[i][0] = a[i];
            }
            for (int j = 1; j < log; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    st[i][j] = func(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
                }
            }
        }

        static int query(int l, int r) {
            int length = r - l + 1;
            int k = 0;
            while ((1 << (k + 1)) <= length) {
                k++;
            }
            return func(st[l][k], st[r - (1 << k) + 1][k]);
        }

        static void printTable(int n) {
            for (int j = 0; j < log; j++) {
                for (int i = 0; i < n; i++) {
                    System.out.print(st[i][j] + " ");
                }
                System.out.println();
            }
        }
    }

    /*
     * ====================================Main=================================
     */

    // static int st[], a[];

    // static void buildTree(int treeIndex, int lo, int hi) {
    // if (hi == lo) {
    // st[treeIndex] = a[lo];
    // return;
    // }
    // int mid = (lo + hi) / 2;
    // buildTree(treeIndex * 2 + 1, lo, mid);
    // buildTree(treeIndex * 2 + 2, mid + 1, hi);
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
    // if (hi == lo) {
    // st[treeIndex] = val;
    // a[arrIndex] = val;
    // return;
    // }
    // int mid = (hi + lo) / 2;
    // if (mid < arrIndex) {
    // update(treeIndex * 2 + 2, mid + 1, hi, arrIndex, val);
    // } else {
    // update(treeIndex * 2 + 1, lo, mid, arrIndex, val);
    // }
    // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
    // }

    // static int query(int treeIndex, int lo, int hi, int l, int r) {
    // if (l <= lo && r >= hi) {
    // return st[treeIndex];
    // }
    // if (l > hi || r < lo) {
    // return 0;
    // }
    // int mid = (hi + lo) / 2;
    // return query(treeIndex * 2 + 1, lo, mid, l, Math.min(mid, r));
    // }

    // static int merge(int a, int b) {
    // return a + b;
    // }

    public static long findKthPositive(long[] A, long k) {
        int l = 0, r = A.length, m;
        while (l < r) {
            m = (l + r) / 2;
            if (A[m] - 1 - m < k)
                l = m + 1;
            else
                r = m;
        }
        return l + k;
    }

    static int[] z_function(char ar[]) {
        int[] z = new int[ar.length];
        z[0] = ar.length;
        int l = 0;
        int r = 0;
        for (int i = 1; i < ar.length; i++) {
            if (r < i) {
                l = i;
                r = i;
                while (r < ar.length && ar[r - l] == ar[r])
                    r++;
                z[i] = r - l;
                r--;
            } else {
                int k = i - l;
                if (z[k] < r - i + 1) {
                    z[i] = z[k];
                } else {
                    l = i;
                    while (r < ar.length && ar[r - l] == ar[r])
                        r++;
                    z[i] = r - l;
                    r--;
                }
            }
        }
        return z;
    }

    static long dp[][][];
    static ArrayList<ArrayList<Integer>> g;
    static int r[] = { 1, -1, 0, 0 }, c[] = { 0, 0, 1, -1 };

    static class Book {
        int t, a, b;

        Book(int t, int a, int b) {
            this.t = t;
            this.a = a;
            this.b = b;
        }
    }

    public static void main(String args[]) throws Exception {
        // File file = new File("D:\\VS Code\\Java\\Output.txt");
        // FileWriter fw = new FileWriter("D:\\VS Code\\Java\\Output.txt");
        int t = 1;
        t = f.nextInt();
        int tc = 1;
        while (t-- != 0) {
            // BufferedReader br = new BufferedReader(new FileReader("PHOBIA.INP"));
            // PrintWriter pw = new PrintWriter(new BufferedWriter(new
            // FileWriter("PHOBIA.OUT")));
            int n = f.nextInt();
            int a = f.nextInt();
            int b = f.nextInt();
            // if (a != 1) {
            //     while (n % a == 0) {
            //         n /= a;
            //     }
            // }
            // int reqPow=0;
            // System.out.println(n);
            // if ((n - 1) % b == 0) {
            // w.write("Yes\n");
            // continue;
            // }

            long power = 1, flag = 0;
            while (n >= power) {

                // System.out.println(n-power);
                if ((n - power) % b == 0) {
                    // reqPow=power;
                    flag = 1;
                    break;
                }
                power *= a;
                if (power == 1)
                    break;
            }
            // if (n - power >= 0 && (n - power) % b == 0) {
            // n -= power;
            // }
            if (flag == 1) {
                w.write("Yes\n");
            } else {
                w.write("No\n");
            }

        }
        w.flush();
    }
}
/*
 * 1+(2+25)+(3+25)+(4+25)+(6+25) 25*9+55 225
 */