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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class Main {

	private static final String NO = "No";
	private static final String YES = "Yes";
	InputStream is;
	PrintWriter out;
	String INPUT = "";

	private static final long MOD = 1000000007;
	private static final int MAXN = 1000000;

	void solve() {
		int T = ni();
		for (int i = 0; i < T; i++) {
			solve(i);
		}
	}

	void solve(int T) {
		int n = ni();
		int m = ni();
		int a[][] = na(n, m);

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (a[i][j] % 2 == (i + j) % 2)
					;
				else
					a[i][j]++;
			}
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++)
				out.print(a[i][j] + " ");
			out.println();
		}
	}

	// a^b
	long power(long a, long b) {
		long x = 1, y = a;
		while (b > 0) {
			if (b % 2 != 0) {
				x = (x * y) % MOD;
			}
			y = (y * y) % MOD;
			b /= 2;
		}
		return x % MOD;
	}

	private long gcd(long a, long b) {
		while (a != 0) {
			long tmp = b % a;
			b = a;
			a = tmp;
		}
		return b;
	}

	void run() throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);

		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if (!INPUT.isEmpty())
			tr(System.currentTimeMillis() - s + "ms");
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n) {
			if (!(isSpaceChar(b)))
				buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private List<Integer> na2(int n) {
		List<Integer> a = new ArrayList<Integer>();
		for (int i = 0; i < n; i++)
			a.add(ni());
		return a;
	}

	private int[][] na(int n, int m) {
		int[][] a = new int[n][];
		for (int i = 0; i < n; i++)
			a[i] = na(m);
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private long[][] nl(int n, int m) {
		long[][] a = new long[n][];
		for (int i = 0; i < n; i++)
			a[i] = nl(m);
		return a;
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	static class CHT {
		long M[], C[];
		int ptr, idx;
		boolean slopeInc, queryMax;

		CHT(int n, boolean isSlopeIncreasing, boolean isQueryMax) {
			M = new long[n + 1];
			C = new long[n + 1];
			slopeInc = isSlopeIncreasing;
			queryMax = isQueryMax;
			ptr = idx = 0;
		}

		boolean bad(int i, int j, int k) {
			if ((slopeInc && queryMax) || (!slopeInc && !queryMax)) {
				return (C[k] - C[i]) / (M[i] - M[k]) <= (C[j] - C[i]) / (M[i] - M[j]); /// (slope dec+query min),(slope
																						/// inc+query max)
			} else {
				return (C[k] - C[i]) * (M[i] - M[j]) >= (C[j] - C[i]) * (M[i] - M[k]); /// (slope dec+query max), (slope
																						/// inc+query min)
			}
		}

		void add(long m, long c) {
			M[idx] = m;
			C[idx] = c;
			++idx;
			while (idx >= 3 && bad(idx - 3, idx - 2, idx - 1)) {
				M[idx - 2] = M[idx - 1];
				C[idx - 2] = C[idx - 1];
				idx--;
			}
		}

		long getY(int i, long x) { // y = mx + c //
			return M[i] * x + C[i];
		}

		/// (slope dec+query min),(slope inc+query max) -> x increasing
		/// (slope dec+query max), (slope inc+query min) -> x decreasing
		long query(long x) {
			if (ptr >= idx) {
				ptr = idx - 1;
			}
			if (queryMax) { // for maximum
				while (ptr < idx - 1 && getY(ptr + 1, x) >= getY(ptr, x))
					ptr++;
				return M[ptr] * x + C[ptr];
			} else { // for minimum
				while (ptr < idx - 1 && getY(ptr + 1, x) <= getY(ptr, x))
					ptr++;
				return M[ptr] * x + C[ptr];
			}
		}

		/// works for random query x
		long query_random_x(long x) {
			return bs(0, idx - 1, x, idx);
		}

		long bs(int st, int ed, long x, int idx) {
			int mid = (st + ed) >> 1;

			if (queryMax) { /// for maximum
				if (mid + 1 < idx && getY(mid + 1, x) > getY(mid, x))
					return bs(mid + 1, ed, x, idx);
				if (mid - 1 >= 0 && getY(mid - 1, x) > getY(mid, x))
					return bs(st, mid - 1, x, idx);
				return getY(mid, x);
			} else { /// for minimum
				if (mid + 1 < idx && getY(mid + 1, x) < getY(mid, x))
					return bs(mid + 1, ed, x, idx);
				if (mid - 1 >= 0 && getY(mid - 1, x) < getY(mid, x))
					return bs(st, mid - 1, x, idx);
				return getY(mid, x);
			}
		}
	}
}