Problem: You are given a matrix a consisting of positive integers. It has n rows and m columns.

Construct a matrix b consisting of positive integers. It should have the same size as a, and the following conditions should be met: 

  * 1 ≤ b_{i,j} ≤ 10^6; 
  * b_{i,j} is a multiple of a_{i,j}; 
  * the absolute value of the difference between numbers in any adjacent pair of cells (two cells that share the same side) in b is equal to k^4 for some integer k ≥ 1 (k is not necessarily the same for all pairs, it is own for each pair). 



We can show that the answer always exists.

Input

The first line contains two integers n and m (2 ≤ n,m ≤ 500).

Each of the following n lines contains m integers. The j-th integer in the i-th line is a_{i,j} (1 ≤ a_{i,j} ≤ 16).

Output

The output should contain n lines each containing m integers. The j-th integer in the i-th line should be b_{i,j}.

Examples

Input


2 2
1 2
2 3


Output


1 2
2 3


Input


2 3
16 16 16
16 16 16


Output


16 32 48
32 48 64


Input


2 2
3 11
12 8


Output


327 583
408 664

Note

In the first example, the matrix a can be used as the matrix b, because the absolute value of the difference between numbers in any adjacent pair of cells is 1 = 1^4.

In the third example: 

  * 327 is a multiple of 3, 583 is a multiple of 11, 408 is a multiple of 12, 664 is a multiple of 8; 
  * |408 - 327| = 3^4, |583 - 327| = 4^4, |664 - 408| = 4^4, |664 - 583| = 3^4. 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public final class Solution {


    static PrintWriter out = new PrintWriter(System.out);
    static FastReader in = new FastReader();
    static long mod = (long) 1e9 + 7;
    static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(1, 0), new Pair(0, -1), new Pair(0, 1)};

    //You are given a matrix 𝑎 consisting of positive integers. It has 𝑛 rows and 𝑚 columns.
    //
    //Construct a matrix 𝑏 consisting of positive integers. It should have the same size as 𝑎, and the following conditions should be met:
    //
    //1≤𝑏𝑖,𝑗≤106;
    //𝑏𝑖,𝑗 is a multiple of 𝑎𝑖,𝑗;
    //the absolute value of the difference between numbers in any adjacent pair of cells (two cells that share the same side) in 𝑏 is equal to 𝑘4 for some integer 𝑘≥1 (𝑘 is not necessarily the same for all pairs, it is own for each pair).
    //We can show that the answer always exists.
    //
    //Input
    //The first line contains two integers 𝑛 and 𝑚 (2≤𝑛,𝑚≤500).
    //
    //Each of the following 𝑛 lines contains 𝑚 integers. The 𝑗-th integer in the 𝑖-th line is 𝑎𝑖,𝑗 (1≤𝑎𝑖,𝑗≤16).
    //
    //Output
    //The output should contain 𝑛 lines each containing 𝑚 integers. The 𝑗-th integer in the 𝑖-th line should be 𝑏𝑖,𝑗.
    // a * x - b * y = k ^ 4

    // 16 16 15 16 15 12 14 16 9 10
    // 11 12 13 14 15 16
    // 16 * 9 * 5 * 7 * 11 * 13

    public static void main(String[] args) {
        int t = 1;

        int mul = 16 * 9 * 5 * 7 * 11 * 13;

        out:
        while (t-- > 0) {
            int n = i();
            int m = i();
            int[][] a = new int[n][m];

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = i();

                    if ((i + j) % 2 == 0) {
                        a[i][j] = (int) (mul + Math.pow(a[i][j], 4));
                    } else {
                        a[i][j] = mul;
                    }
                    out.print(a[i][j] + " ");
                }
                out.println();
            }
        }
        out.flush();
    }

    static boolean isPS(double number) {
        double sqrt = Math.sqrt(number);
        return ((sqrt - Math.floor(sqrt)) == 0);
    }

    static int sd(long i) {
        int d = 0;
        while (i > 0) {
            d += i % 10;
            i = i / 10;
        }
        return d;
    }

    static int[] leastPrime;

    static void sieveLinear(int N) {
        int[] primes = new int[N];
        int idx = 0;
        leastPrime = new int[N + 1];
        for (int i = 2; i <= N; i++) {
            if (leastPrime[i] == 0) {
                primes[idx++] = i;
                leastPrime[i] = i;
            }
            int curLP = leastPrime[i];
            for (int j = 0; j < idx; j++) {
                int p = primes[j];
                if (p > curLP || (long) p * i > N) {
                    break;
                } else {
                    leastPrime[p * i] = p;
                }
            }
        }
    }


    static int lower(long A[], long x) {
        int l = -1, r = A.length;
        while (r - l > 1) {
            int m = (l + r) / 2;
            if (A[m] >= x) {
                r = m;
            } else {
                l = m;
            }
        }
        return r;
    }

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

    static void swap(int A[], int a, int b) {
        int t = A[a];
        A[a] = A[b];
        A[b] = t;
    }

    static int lowerBound(int A[], int low, int high, int x) {
        if (low > high) {
            if (x >= A[high]) {
                return A[high];
            }
        }

        int mid = (low + high) / 2;

        if (A[mid] == x) {
            return A[mid];
        }

        if (mid > 0 && A[mid - 1] <= x && x < A[mid]) {
            return A[mid - 1];
        }

        if (x < A[mid]) {
            return lowerBound(A, low, mid - 1, x);
        }

        return lowerBound(A, mid + 1, high, x);
    }


    static long pow(long a, long b) {
        long pow = 1;
        long x = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                pow = (pow * x) % mod;
            }
            x = (x * x) % mod;
            b /= 2;
        }
        return pow;
    }

    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 (int i = 5; i * i <= N; i = i + 6) {
            if (N % i == 0 || N % (i + 2) == 0) {
                return false;
            }
        }
        return true;
    }

    static void print(char A[]) {
        for (char c : A) {
            out.print(c);
        }
        out.println();
    }

    static void print(boolean A[]) {
        for (boolean c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(int A[]) {
        for (int c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(long A[]) {
        for (long i : A) {
            out.print(i + " ");
        }
        out.println();

    }

    static void print(List<Integer> A) {
        for (int a : A) {
            out.print(a + " ");
        }
    }

    static void printYes() {
        out.println("YES");
    }

    static void printNo() {
        out.println("NO");
    }

    static int i() {
        return in.nextInt();
    }

    static long l() {
        return in.nextLong();
    }

    static String s() {
        return in.nextLine();
    }

    static int[] input(int N) {
        int A[] = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N) {
        long A[] = new long[N];
        for (int i = 0; i < A.length; i++) {
            A[i] = in.nextLong();
        }
        return A;
    }

    static int GCD(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

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

}

class BIT {

    int n;
    int[] tree;

    public BIT(int n) {
        this.n = n;
        this.tree = new int[n + 1];
    }

    public static int lowbit(int x) {
        return x & (-x);
    }

    public void update(int x) {
        while (x <= n) {
            ++tree[x];
            x += lowbit(x);
        }
    }

    public int query(int x) {
        int ans = 0;
        while (x > 0) {
            ans += tree[x];
            x -= lowbit(x);
        }
        return ans;
    }

    public int query(int x, int y) {
        return query(y) - query(x - 1);
    }
}

class SegmentTree {

    long[] t;

    public SegmentTree(int n) {
        t = new long[n + n];
        Arrays.fill(t, Long.MIN_VALUE);
    }

    public long get(int i) {
        return t[i + t.length / 2];
    }

    public void add(int i, long value) {
        i += t.length / 2;
        t[i] = value;
        for (; i > 1; i >>= 1) {
            t[i >> 1] = Math.max(t[i], t[i ^ 1]);
        }
    }

    // max[a, b]
    public long max(int a, int b) {
        long res = Long.MIN_VALUE;
        for (a += t.length / 2, b += t.length / 2; a <= b; a = (a + 1) >> 1, b = (b - 1) >> 1) {
            if ((a & 1) != 0) {
                res = Math.max(res, t[a]);
            }
            if ((b & 1) == 0) {
                res = Math.max(res, t[b]);
            }
        }
        return res;
    }
}

class Pair {

    int i, j;

    Pair(int i, int j) {
        this.i = i;
        this.j = j;
    }

}

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;
    }
}