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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;


public class PlusAndMultiply {


    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread (null, new TaskAdapter (), "", 1 << 29);
        thread.start ();
        thread.join ();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput (inputStream);
            FastOutput out = new FastOutput (outputStream);
            Solution solver = new Solution ();
            solver.solve (1, in, out);
            out.close ();
        }
    }

    static class Solution {
        Debug debug = new Debug (true);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int test= in.ri ();

            while (test-->0){
                long n= in.rl ();
                long a= in.rl ();
                long b= in.rl ();
                long cur=1;
                boolean flag=false;
                while (cur<=n){
                    if((n-cur)%b==0){
                        flag=true;
                        break;
                    }
                    cur*=a;
//                    debug.debug ("cur",cur);
                    if(cur==1) break;

                }
                out.append (flag?"Yes\n":"No\n");


            }

        }

    }


    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder (THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append (csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append (csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length () < THRESHOLD) {
                return;
            }
            flush ();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this (new OutputStreamWriter (os));
        }

        public FastOutput append(char c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput append(String c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput println(String c) {
            return append (c).println ();
        }

        public FastOutput println() {
            return append ('\n');
        }

        final <T> void prt(T a) {
            append (a + " ");
        }

        final <T> void prtl(T a) {
            append (a + "\n");
        }

        public FastOutput flush() {
            try {
                // boolean success = false;
                // if (stringBuilderValueField != null) {
                //  try {
                //  char[] value = (char[]) stringBuilderValueField.get(cache);
                //          os.write(value, 0, cache.length());
                //                  success = true;
                //          } catch (Exception e) {
                //      }
                //  }
                //  if (!success) {
                //  }
                os.append (cache);
                os.flush ();
                cache.setLength (0);
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
            return this;
        }

        public void close() {
            flush ();
            try {
                os.close ();
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }

        public String toString() {
            return cache.toString ();
        }

        public FastOutput printf(String format, Object... args) {
            return append (String.format (format, args));
        }

        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

    }


    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder (1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private SpaceCharFilter filter;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        public void populate(int[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readInt ();
            }
        }

        public void populate(long[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readLong ();
            }
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read (buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read ();
            }
        }

        public String next() {
            return readString ();
        }

        public int ri() {
            return readInt ();
        }

        public int readInt() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            int val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long readLong() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            long val = 0L;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long rl() {
            return readLong ();
        }

        public String readString(StringBuilder builder) {
            skipBlank ();

            while (next > 32) {
                builder.append ((char) next);
                next = read ();
            }

            return builder.toString ();
        }

        public String readString() {
            defaultStringBuf.setLength (0);
            return readString (defaultStringBuf);
        }

        public int rs(char[] data, int offset) {
            return readString (data, offset);
        }

        public int rs(char[] data) {
            return rs (data, 0);
        }

        public int readString(char[] data, int offset) {
            skipBlank ();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read ();
            }

            return offset - originalOffset;
        }

        public char rc() {
            return readChar ();
        }

        public char readChar() {
            skipBlank ();
            char c = (char) next;
            next = read ();
            return c;
        }

        public double rd() {
            return nextDouble ();
        }

        public double nextDouble() {
            int c = read ();
            while (isSpaceChar (c))
                c = read ();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read ();
            }
            double res = 0;
            while (!isSpaceChar (c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow (10, readInt ());
                if (c < '0' || c > '9')
                    throw new InputMismatchException ();
                res *= 10;
                res += c - '0';
                c = read ();
            }
            if (c == '.') {
                c = read ();
                double m = 1;
                while (!isSpaceChar (c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow (10, readInt ());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException ();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read ();
                }
            }
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar (c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }

    }


    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager () == null;
        }

        public Debug debug(String name, Object x) {
            return debug (name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass ().isArray ()) {
                    out.append (name);
                    for (int i : indexes) {
                        out.printf ("[%d]", i);
                    }
                    out.append ("=").append ("" + x);
                    out.println ();
                } else {
                    indexes = Arrays.copyOf (indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }
}