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.*;
import java.util.HashSet;

public class PlusAndMultiply2 {
    static class InputReader {

        /**
         * The default size of the InputReader's buffer is 2^16 -> 65,536 characters
         */
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16; // Change this to increase your input size //

        /**
         * The default stream for the InputReader is standard input.
         */
        private static final InputStream DEFAULT_STREAM = System.in;

        /**
         * The maximum number of accurate decimal digits the method {@link #nextDoubleFast() nextDoubleFast()} can read.
         * Currently this value is set to 21 because it is the maximum number of digits a double precision float can have at the moment.
         */
        private static final int MAX_DECIMAL_PRECISION = 21;

        // 'c' is used to refer to the current character in the stream
        private int c;

        // Variables associated with the byte buffer.
        private byte[] buf;
        private int bufferSize, bufIndex, numBytesRead;

        private InputStream stream;

        // End Of File (EOF) character
        private static final byte EOF = -1;

        // New line character: '\n'
        private static final byte NEW_LINE = 10;

        // Carriage return character: '\r'
        private static final byte CARRIAGE_RETURN = 13;

        // Space character: ' '
        private static final byte SPACE = 32;

        // Dash character: '-'
        private static final byte DASH = 45;

        // Dot character: '.'
        private static final byte DOT = 46;

        // A reusable character buffer when reading string data.
        private char[] charBuffer;

        // Primitive data type lookup tables used for optimizations
        private static byte[] bytes = new byte[58];
        private static int[] ints = new int[58];
        private static char[] chars = new char[128];

        static {
            char ch = ' ';
            int value = 0;
            byte _byte = 0;
            for (int i = 48; i < 58; i++) bytes[i] = _byte++;
            for (int i = 48; i < 58; i++) ints[i] = value++;
            for (int i = 32; i < 128; i++) chars[i] = ch++;
        }

        // Primitive double lookup table used for optimizations.
        private static final double[][] doubles = {
                {0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d, 0.0000000000d, 0.00000000000d, 0.000000000000d, 0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d, 0.00000000000000000d, 0.000000000000000000d, 0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d},
                {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d, 0.0000000001d, 0.00000000001d, 0.000000000001d, 0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d, 0.00000000000000001d, 0.000000000000000001d, 0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d},
                {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d, 0.0000000002d, 0.00000000002d, 0.000000000002d, 0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d, 0.00000000000000002d, 0.000000000000000002d, 0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d},
                {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d, 0.0000000003d, 0.00000000003d, 0.000000000003d, 0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d, 0.00000000000000003d, 0.000000000000000003d, 0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d},
                {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d, 0.0000000004d, 0.00000000004d, 0.000000000004d, 0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d, 0.00000000000000004d, 0.000000000000000004d, 0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d},
                {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d, 0.0000000005d, 0.00000000005d, 0.000000000005d, 0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d, 0.00000000000000005d, 0.000000000000000005d, 0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d},
                {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d, 0.0000000006d, 0.00000000006d, 0.000000000006d, 0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d, 0.00000000000000006d, 0.000000000000000006d, 0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d},
                {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d, 0.0000000007d, 0.00000000007d, 0.000000000007d, 0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d, 0.00000000000000007d, 0.000000000000000007d, 0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d},
                {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d, 0.0000000008d, 0.00000000008d, 0.000000000008d, 0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d, 0.00000000000000008d, 0.000000000000000008d, 0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d},
                {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d, 0.0000000009d, 0.00000000009d, 0.000000000009d, 0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d, 0.00000000000000009d, 0.000000000000000009d, 0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}
        };

        /**
         * Create an InputReader that reads from standard input.
         */
        public InputReader() {
            this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE);
        }

        /**
         * Create an InputReader that reads from standard input.
         *
         * @param bufferSize The buffer size for this input reader.
         */
        public InputReader(int bufferSize) {
            this(DEFAULT_STREAM, bufferSize);
        }

        /**
         * Create an InputReader that reads from standard input.
         *
         * @param stream Takes an InputStream as a parameter to read from.
         */
        public InputReader(InputStream stream) {
            this(stream, DEFAULT_BUFFER_SIZE);
        }

        /**
         * Create an InputReader that reads from standard input.
         *
         * @param stream     Takes an {@link InputStream#InputStream() InputStream} as a parameter to read from.
         * @param bufferSize The size of the buffer to use.
         */
        public InputReader(InputStream stream, int bufferSize) {
            if (stream == null || bufferSize <= 0)
                throw new IllegalArgumentException();
            buf = new byte[bufferSize];
            charBuffer = new char[128];
            this.bufferSize = bufferSize;
            this.stream = stream;
        }

        /**
         * Reads a single character from the input stream.
         *
         * @return Returns the byte value of the next character in the buffer and EOF
         * at the end of the stream.
         * @throws IOException throws exception if there is no more data to read
         */
        private byte read() throws IOException {

            if (numBytesRead == EOF) throw new IOException();

            if (bufIndex >= numBytesRead) {
                bufIndex = 0;
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF)
                    return EOF;
            }

            return buf[bufIndex++];
        }

        /**
         * Read values from the input stream until you reach a character with a
         * higher ASCII value than 'token'.
         *
         * @param token The token is a value which we use to stop reading junk out of
         *              the stream.
         * @return Returns 0 if a value greater than the token was reached or -1 if
         * the end of the stream was reached.
         * @throws IOException Throws exception at end of stream.
         */
        private int readJunk(int token) throws IOException {

            if (numBytesRead == EOF) return EOF;

            // Seek to the first valid position index
            do {

                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] > token) return 0;
                    bufIndex++;
                }

                // reload buffer
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF) return EOF;
                bufIndex = 0;

            } while (true);

        }

        /**
         * Reads a single byte from the input stream.
         *
         * @return The next byte in the input stream
         * @throws IOException Throws exception at end of stream.
         */
        public byte nextByte() throws IOException {
            return (byte) nextInt();
        }

        /**
         * Reads a 32 bit signed integer from input stream.
         *
         * @return The next integer value in the stream.
         * @throws IOException Throws exception at end of stream.
         */
        public int nextInt() throws IOException {

            if (readJunk(DASH - 1) == EOF) throw new IOException();
            int sgn = 1, res = 0;

            c = buf[bufIndex];
            if (c == DASH) {
                sgn = -1;
                bufIndex++;
            }

            do {

                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] > SPACE) {
                        res = (res << 3) + (res << 1);
                        res += ints[buf[bufIndex++]];
                    } else {
                        bufIndex++;
                        return res * sgn;
                    }
                }

                // Reload buffer
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF) return res * sgn;
                bufIndex = 0;

            } while (true);

        }

        /**
         * Reads a 64 bit signed long from input stream.
         *
         * @return The next long value in the stream.
         * @throws IOException Throws exception at end of stream.
         */
        public long nextLong() throws IOException {

            if (readJunk(DASH - 1) == EOF) throw new IOException();
            int sgn = 1;
            long res = 0L;
            c = buf[bufIndex];
            if (c == DASH) {
                sgn = -1;
                bufIndex++;
            }

            do {

                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] > SPACE) {
                        res = (res << 3) + (res << 1);
                        res += ints[buf[bufIndex++]];
                    } else {
                        bufIndex++;
                        return res * sgn;
                    }
                }

                // Reload buffer
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF) return res * sgn;
                bufIndex = 0;

            } while (true);

        }

        /**
         * Doubles the size of the internal char buffer for strings
         */
        private void doubleCharBufferSize() {
            char[] newBuffer = new char[charBuffer.length << 1];
            for (int i = 0; i < charBuffer.length; i++) newBuffer[i] = charBuffer[i];
            charBuffer = newBuffer;
        }

        /**
         * Reads a line from the input stream.
         *
         * @return Returns a line from the input stream in the form a String not
         * including the new line character. Returns <code>null</code> when there are
         * no more lines.
         * @throws IOException Throws IOException when something terrible happens.
         */
        public String nextLine() throws IOException {

            try {
                c = read();
            } catch (IOException e) {
                return null;
            }
            if (c == NEW_LINE) return ""; // Empty line
            if (c == EOF) return null; // EOF

            int i = 0;
            charBuffer[i++] = (char) c;

            do {

                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] != NEW_LINE && buf[bufIndex] != CARRIAGE_RETURN) {
                        if (i == charBuffer.length) doubleCharBufferSize();
                        charBuffer[i++] = (char) buf[bufIndex++];
                    } else {
                        if(buf[bufIndex] == CARRIAGE_RETURN) bufIndex++;
                        bufIndex++;
                        return new String(charBuffer, 0, i);
                    }
                }

                // Reload buffer
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF)
                    return new String(charBuffer, 0, i);
                bufIndex = 0;

            } while (true);

        }

        // Reads a string of characters from the input stream.
        // The delimiter separating a string of characters is set to be:
        // any ASCII value <= 32 meaning any spaces, new lines, EOF, tabs...
        public String nextString() throws IOException {
            if (numBytesRead == EOF) return null;
            if (readJunk(SPACE) == EOF) return null;

            for (int i = 0; ; ) {
                while (bufIndex < numBytesRead) {
                    if (buf[bufIndex] > SPACE) {
                        if (i == charBuffer.length) doubleCharBufferSize();
                        charBuffer[i++] = (char) buf[bufIndex++];
                    } else {
                        bufIndex++;
                        return new String(charBuffer, 0, i);
                    }
                }

                // Reload buffer
                numBytesRead = stream.read(buf);
                if (numBytesRead == EOF) return new String(charBuffer, 0, i);
                bufIndex = 0;
            }
        }

        // Returns an exact value a double value from the input stream.
        public double nextDouble() throws IOException {
            String doubleVal = nextString();
            if (doubleVal == null) throw new IOException();
            return Double.valueOf(doubleVal);
        }

        // Very quickly reads a double value from the input stream (~3x faster than nextDouble()). However,
        // this method may provide a slightly less accurate reading than .nextDouble() if there are a lot
        // of digits (~16+). In particular, it will only read double values with at most 21 digits after
        // the decimal point and the reading my be as inaccurate as ~5*10^-16 from the true value.
        public double nextDoubleFast() throws IOException {
            c = read();
            int sgn = 1;
            while (c <= SPACE) c = read(); // while c is either: ' ', '\n', EOF
            if (c == DASH) {
                sgn = -1;
                c = read();
            }
            double res = 0.0;
            // while c is not: ' ', '\n', '.' or -1
            while (c > DOT) {
                res *= 10.0;
                res += ints[c];
                c = read();
            }
            if (c == DOT) {
                int i = 0;
                c = read();
                // while c is digit and we are less than the maximum decimal precision
                while (c > SPACE && i < MAX_DECIMAL_PRECISION) {
                    res += doubles[ints[c]][i++];
                    c = read();
                }
            }
            return res * sgn;
        }

        // Read an array of n byte values
        public byte[] nextByteArray(int n) throws IOException {
            byte[] ar = new byte[n];
            for (int i = 0; i < n; i++) ar[i] = nextByte();
            return ar;
        }

        // Read an integer array of size n
        public int[] nextIntArray(int n) throws IOException {
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) ar[i] = nextInt();
            return ar;
        }

        // Read a long array of size n
        public long[] nextLongArray(int n) throws IOException {
            long[] ar = new long[n];
            for (int i = 0; i < n; i++) ar[i] = nextLong();
            return ar;
        }

        // read an of doubles of size n
        public double[] nextDoubleArray(int n) throws IOException {
            double[] ar = new double[n];
            for (int i = 0; i < n; i++) ar[i] = nextDouble();
            return ar;
        }

        // Quickly read an array of doubles
        public double[] nextDoubleArrayFast(int n) throws IOException {
            double[] ar = new double[n];
            for (int i = 0; i < n; i++) ar[i] = nextDoubleFast();
            return ar;
        }

        // Read a string array of size n
        public String[] nextStringArray(int n) throws IOException {
            String[] ar = new String[n];
            for (int i = 0; i < n; i++) {
                String str = nextString();
                if (str == null) throw new IOException();
                ar[i] = str;
            }
            return ar;
        }

        // Read a 1-based byte array of size n+1
        public byte[] nextByteArray1(int n) throws IOException {
            byte[] ar = new byte[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextByte();
            return ar;
        }

        // Read a 1-based integer array of size n+1
        public int[] nextIntArray1(int n) throws IOException {
            int[] ar = new int[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextInt();
            return ar;
        }

        // Read a 1-based long array of size n+1
        public long[] nextLongArray1(int n) throws IOException {
            long[] ar = new long[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextLong();
            return ar;
        }

        // Read a 1-based double array of size n+1
        public double[] nextDoubleArray1(int n) throws IOException {
            double[] ar = new double[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextDouble();
            return ar;
        }

        // Quickly read a 1-based double array of size n+1
        public double[] nextDoubleArrayFast1(int n) throws IOException {
            double[] ar = new double[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextDoubleFast();
            return ar;
        }

        // Read a 1-based string array of size n+1
        public String[] nextStringArray1(int n) throws IOException {
            String[] ar = new String[n + 1];
            for (int i = 1; i <= n; i++) ar[i] = nextString();
            return ar;
        }

        // Read a two dimensional matrix of bytes of size rows x cols
        public byte[][] nextByteMatrix(int rows, int cols) throws IOException {
            byte[][] matrix = new byte[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextByte();
            return matrix;
        }

        // Read a two dimensional matrix of ints of size rows x cols
        public int[][] nextIntMatrix(int rows, int cols) throws IOException {
            int[][] matrix = new int[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextInt();
            return matrix;
        }

        // Read a two dimensional matrix of longs of size rows x cols
        public long[][] nextLongMatrix(int rows, int cols) throws IOException {
            long[][] matrix = new long[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextLong();
            return matrix;
        }

        // Read a two dimensional matrix of doubles of size rows x cols
        public double[][] nextDoubleMatrix(int rows, int cols) throws IOException {
            double[][] matrix = new double[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextDouble();
            return matrix;
        }

        // Quickly read a two dimensional matrix of doubles of size rows x cols
        public double[][] nextDoubleMatrixFast(int rows, int cols) throws IOException {
            double[][] matrix = new double[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextDoubleFast();
            return matrix;
        }

        // Read a two dimensional matrix of Strings of size rows x cols
        public String[][] nextStringMatrix(int rows, int cols) throws IOException {
            String[][] matrix = new String[rows][cols];
            for (int i = 0; i < rows; i++)
                for (int j = 0; j < cols; j++)
                    matrix[i][j] = nextString();
            return matrix;
        }

        // Read a 1-based two dimensional matrix of bytes of size rows x cols
        public byte[][] nextByteMatrix1(int rows, int cols) throws IOException {
            byte[][] matrix = new byte[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextByte();
            return matrix;
        }

        // Read a 1-based two dimensional matrix of ints of size rows x cols
        public int[][] nextIntMatrix1(int rows, int cols) throws IOException {
            int[][] matrix = new int[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextInt();
            return matrix;
        }

        // Read a 1-based two dimensional matrix of longs of size rows x cols
        public long[][] nextLongMatrix1(int rows, int cols) throws IOException {
            long[][] matrix = new long[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextLong();
            return matrix;
        }

        // Read a 1-based two dimensional matrix of doubles of size rows x cols
        public double[][] nextDoubleMatrix1(int rows, int cols) throws IOException {
            double[][] matrix = new double[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextDouble();
            return matrix;
        }

        // Quickly read a 1-based two dimensional matrix of doubles of size rows x cols
        public double[][] nextDoubleMatrixFast1(int rows, int cols) throws IOException {
            double[][] matrix = new double[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextDoubleFast();
            return matrix;
        }

        // Read a 1-based two dimensional matrix of Strings of size rows x cols
        public String[][] nextStringMatrix1(int rows, int cols) throws IOException {
            String[][] matrix = new String[rows + 1][cols + 1];
            for (int i = 1; i <= rows; i++)
                for (int j = 1; j <= cols; j++)
                    matrix[i][j] = nextString();
            return matrix;
        }

        // Closes the input stream
        public void close() throws IOException {
            stream.close();
        }
    }

    // region variables
    static InputReader sc = new InputReader();
    static OutputStream outputStream = System.out;
    static PrintWriter w = new PrintWriter(outputStream);
    static long timeStart;
    // endregion

    private static void initiateIO()
            throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            try {
                w = new PrintWriter("output.txt");
                sc = new InputReader(new FileInputStream("input.txt"));
            } catch (Exception e) {
                throw new IOException();
            }
        }
    }

    public static void main(String[] args)
            throws IOException {

        initiateIO();

        int t = sc.nextInt();
        while(t-- > 0) {
            solve();
        }

        w.close();

    }

    static void solve() throws IOException {
        long n = sc.nextLong();
        long a = sc.nextLong();
        long b = sc.nextLong();

        if(a == 1) {
            if((n-1) % b == 0) {
                w.println("YES");
            } else w.println("NO");
            return;
        }

        long curr = 1;

        while(curr <= n) {
            if((n-curr) % b == 0) {
                w.println("YES");
                return;
            }
            curr *= a;
        }

        w.println("NO");
    }
}