Problem: Artem is building a new robot. He has a matrix a consisting of n rows and m columns. The cell located on the i-th row from the top and the j-th column from the left has a value a_{i,j} written in it. 

If two adjacent cells contain the same value, the robot will break. A matrix is called good if no two adjacent cells contain the same value, where two cells are called adjacent if they share a side. 

Artem wants to increment the values in some cells by one to make a good.

More formally, find a good matrix b that satisfies the following condition — 

  * For all valid (i,j), either b_{i,j} = a_{i,j} or b_{i,j} = a_{i,j}+1. 



For the constraints of this problem, it can be shown that such a matrix b always exists. If there are several such tables, you can output any of them. Please note that you do not have to minimize the number of increments.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10). Description of the test cases follows.

The first line of each test case contains two integers n, m (1 ≤ n ≤ 100, 1 ≤ m ≤ 100) — the number of rows and columns, respectively.

The following n lines each contain m integers. The j-th integer in the i-th line is a_{i,j} (1 ≤ a_{i,j} ≤ 10^9).

Output

For each case, output n lines each containing m integers. The j-th integer in the i-th line is b_{i,j}.

Example

Input


3
3 2
1 2
4 5
7 8
2 2
1 1
3 3
2 2
1 3
2 2


Output


1 2
5 6
7 8
2 1
4 3
2 4
3 2

Note

In all the cases, you can verify that no two adjacent cells have the same value and that b is the same as a with some values incremented by one. 

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 EngineerArtem {


    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 {
        static final Debug debug = new Debug (true);

        public void solve(int testNumber, FastInput in, FastOutput out) {

            int test = in.ri ();

            while (test-- > 0) {
                int n = in.ri ();
                int m = in.ri ();

                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < m; j++) {
                        int x= in.ri ();
                        if(x%2==(i+j)%2)
                            out.prt (x);
                        else
                            out.prt (x+1);
                    }
                    out.println ();
                }
            }
        }

    }




    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 {
                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 static final int EOF = -1;
        private SpaceCharFilter filter;
        private int bufOffset;
        private int next;
        private int bufLen;

        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 char[] rsc() {
            return readString ().toCharArray ();
        }


        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);
        }


        public boolean hasMore() {
            skipBlank ();
            return next != EOF;
        }


    }


    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, long x) {
            if (offline) {
                debug (name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf ("%s=%s", name, x);
                out.println ();
            }
            return this;
        }

        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;
        }

    }
}