You are given four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50). Find any such rectangular matrix of size n × m that satisfies all of the following conditions:

  * each row of the matrix contains exactly a ones; 
  * each column of the matrix contains exactly b ones; 
  * all other elements are zeros. 



If the desired matrix does not exist, indicate this.

For example, for n=3, m=6, a=2, b=1, there exists a matrix satisfying the conditions above:

$$$ \begin{vmatrix} 0 & 1 & 0 & 0 & 0 & 1 \\\ 1 & 0 & 0 & 1 & 0 & 0 \\\ 0 & 0 & 1 & 0 & 1 & 0 \end{vmatrix} $$$

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.

Each test case is described by four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50), where n and m are the sizes of the matrix, and a and b are the number of ones for rows and columns, respectively.

Output

For each test case print:

  * "YES" (without quotes) and the required matrix (if there are several answers, print any) if it exists, or 
  * "NO" (without quotes) if it does not exist. 



To print the matrix n × m, print n rows, each of which consists of m numbers 0 or 1 describing a row of the matrix. Numbers must be printed without spaces.

Example

Input


5
3 6 2 1
2 2 2 1
2 2 2 2
4 4 2 2
2 1 1 2


Output


YES
010001
100100
001010
NO
YES
11
11
YES
1100
1100
0011
0011
YES
1
1
import java.io.*;
import java.util.*;

public class Solution {

    public static void main(String args[]) throws IOException {
        InOut inout = new InOut();
        Resolver resolver = new Resolver(inout);
        resolver.solve();
        inout.flush();
    }

    private static class Resolver {

        final long LONG_INF = (long) 1e18;
        final int INF = 1000000007;
        final int MOD = 998244353;
        long f[];
        InOut inout;

        Resolver(InOut inout) {
            this.inout = inout;
        }

        void initF(int n) {
            f = new long[n + 1];
            f[1] = 1;
            for (int i = 2; i <= n; i++) {
                f[i] = (f[i - 1] * i) % MOD;
            }
        }

        int[] dfs(int f, int dst, boolean vis[]) {
            int n0 = 1 - dst;
            int n1 = dst;
            vis[f] = true;
            for (int i = 0; i < edges[f].size(); i++) {
                int t = edges[f].get(i)[0];
                if (vis[t]) {
                    continue;
                }
                int tmp[] = dfs(t, (dst + 1) % 2, vis);
                n0 += tmp[0];
                n1 += tmp[1];
            }
            return new int[] {n0, n1};
        }

        int dfs2(int f, int dst, int n1, int color[], boolean vis[]) {
            int cnt = 0;
            vis[f] = true;
            if (dst % 2 == 0) {
                color[f] = 2;
            } else {
                if (n1 > 0) {
                    color[f] = 1;
                    n1--;
                    cnt++;
                } else {
                    color[f] = 3;
                }
            }
            for (int i = 0; i < edges[f].size(); i++) {
                int t = edges[f].get(i)[0];
                if (vis[t]) {
                    continue;
                }
                cnt += dfs2(t, dst + 1, n1, color, vis);
            }
            return cnt;
        }

        void solve() throws IOException {
            int tt = 1;
            boolean hvt = true;
            if (hvt) {
                tt = nextInt();
            }
            for (int cs = 1; cs <= tt; cs++) {
                int n = nextInt();
                int m = nextInt();
                int a = nextInt();
                int b = nextInt();
                if (a > m || b > n || a * n != b * m) {
                    format("NO\n");
                    continue;
                }
                int res[][] = new int[n][m];
                int lft = a;
                int j = 0;
                for (int i = 0; i < n; i++) {
                    for (int k = 0; k < lft; k++) {
                        res[i][j] = 1;
                        j = (j + 1) % m;
                    }
                }
                format("YES\n");
                for (int i = 0; i < n; i++) {
                    for (int k = 0; k < m; k++) {
                        format("%d", res[i][k]);
                    }
                    format("\n");
                }
            }
        }

        String next(int n) throws IOException {
            return inout.next(n);
        }

        int nextInt() throws IOException {
            return inout.nextInt();
        }

        long nextLong(int n) throws IOException {
            return inout.nextLong(n);
        }

        void print(String s, boolean nextLine) {
            inout.print(s, nextLine);
        }

        void format(String format, Object... obj) {
            inout.format(format, obj);
        }

        void flush() {
            inout.flush();
        }

        void swap(int a[], int i, int j) {
            a[i] ^= a[j];
            a[j] ^= a[i];
            a[i] ^= a[j];
        }

        boolean topSort() {
            int n = edges.length - 1;
            int d[] = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 0; j < edges[i].size(); j++) {
                    d[edges[i].get(j)[0]]++;
                }
            }
            List<Integer> list = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                if (d[i] == 0) {
                    list.add(i);
                }
            }
            for (int i = 0; i < list.size(); i++) {
                for (int j = 0; j < edges[list.get(i)].size(); j++) {
                    int t = edges[list.get(i)].get(j)[0];
                    d[t]--;
                    if (d[t] == 0) {
                        list.add(t);
                    }
                }
            }
            return list.size() == n;
        }

        class BinaryIndexedTree {

            int n = 1;
            long C[];

            BinaryIndexedTree(int sz) {
                while (n <= sz) {
                    n <<= 1;
                }
                C = new long[n];
            }

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

            void add(int x, long val) {
                while (x < n) {
                    C[x] += val;
                    x += lowbit(x);
                }
            }

            long getSum(int x) {
                long res = 0;
                while (x > 0) {
                    res += C[x];
                    x -= lowbit(x);
                }
                return res;
            }

            int binSearch(long sum) {
                if (sum == 0) {
                    return 0;
                }
                int n = C.length;
                int mx = 1;
                while (mx < n) {
                    mx <<= 1;
                }
                int res = 0;
                for (int i = mx / 2; i >= 1; i >>= 1) {
                    if (C[res + i] < sum) {
                        sum -= C[res + i];
                        res += i;
                    }
                }
                return res + 1;
            }
        }

        //Binary tree
        class TreeNode {
            int val;
            int tier = -1;
            TreeNode parent;
            TreeNode left;
            TreeNode right;

            TreeNode(int val) {
                this.val = val;
            }
        }

        //binary tree dfs
        void tierTree(TreeNode root) {
            if (null == root) {
                return;
            }
            if (null != root.parent) {
                root.tier = root.parent.tier + 1;
            } else {
                root.tier = 0;
            }
            tierTree(root.left);
            tierTree(root.right);
        }

        //LCA start
        TreeNode[][] lca;
        TreeNode[] tree;

        void lcaDfsTree(TreeNode root) {
            if (null == root) {
                return;
            }
            tree[root.val] = root;
            TreeNode nxt = root.parent;
            int idx = 0;
            while (null != nxt) {
                lca[root.val][idx] = nxt;
                nxt = lca[nxt.val][idx];
                idx++;
            }
            lcaDfsTree(root.left);
            lcaDfsTree(root.right);
        }

        TreeNode lcaTree(TreeNode root, int n, TreeNode x, TreeNode y) {
            if (null == root) {
                return null;
            }
            if (-1 == root.tier) {
                tree = new TreeNode[n + 1];
                tierTree(root);
            }
            if (null == lca) {
                lca = new TreeNode[n + 1][31];
                lcaDfsTree(root);
            }
            int z = Math.abs(x.tier - y.tier);
            int xx = x.tier > y.tier ? x.val : y.val;
            while (z > 0) {
                final int zz = z;
                int l = (int) binSearch(0, 31
                        , k -> zz < (1 << k));
                xx = lca[xx][l].val;
                z -= 1 << l;
            }
            int yy = y.val;
            if (x.tier <= y.tier) {
                yy = x.val;
            }
            while (xx != yy) {
                final int xxx = xx;
                final int yyy = yy;
                int l = (int) binSearch(0, 31
                        , k -> (1 << k) <= tree[xxx].tier && lca[xxx][(int) k] != lca[yyy][(int) k]);
                xx = lca[xx][l].val;
                yy = lca[yy][l].val;
            }
            return tree[xx];
        }
        //LCA end

        //graph
        List<int[]> edges[];

        void initGraph(int n, int m, boolean hasW, boolean directed) throws IOException {
            edges = new List[n + 1];
            for (int i = 1; i <= n; i++) {
                edges[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                int f = nextInt();
                int t = nextInt();
                int w = hasW ? nextInt() : 0;
                edges[f].add(new int[]{t, w});
                if (!directed) {
                    edges[t].add(new int[]{f, w});
                }
            }
        }

        long binSearch(long l, long r, BinSearch sort) {
            while (l < r) {
                long m = l + (r - l) / 2;
                if (sort.binSearchCmp(m)) {
                    l = m + 1;
                } else {
                    r = m;
                }
            }
            return l;
        }

        void getDiv(Map<Integer, Integer> map, int n) {
            int sqrt = (int) Math.sqrt(n);
            for (int i = sqrt; i >= 2; i--) {
                if (n % i == 0) {
                    getDiv(map, i);
                    getDiv(map, n / i);
                    return;
                }
            }
            map.put(n, map.getOrDefault(n, 0) + 1);
        }

        boolean[] generatePrime(int n) {
            boolean p[] = new boolean[n + 1];
            p[2] = true;

            for (int i = 3; i <= n; i += 2) {
                p[i] = true;
            }

            for (int i = 3; i <= Math.sqrt(n); i += 2) {
                if (!p[i]) {
                    continue;
                }
                for (int j = i * i; j <= n; j += i << 1) {
                    p[j] = false;
                }
            }
            return p;
        }

        boolean isPrime(long n) { //determines if n is a prime number
            int p[] = {2, 3, 5, 233, 331};
            int pn = p.length;
            long s = 0, t = n - 1;//n - 1 = 2^s * t
            while ((t & 1) == 0) {
                t >>= 1;
                ++s;
            }
            for (int i = 0; i < pn; ++i) {
                if (n == p[i]) {
                    return true;
                }
                long pt = pow(p[i], t, n);
                for (int j = 0; j < s; ++j) {
                    long cur = llMod(pt, pt, n);
                    if (cur == 1 && pt != 1 && pt != n - 1) {
                        return false;
                    }
                    pt = cur;
                }
                if (pt != 1) {
                    return false;
                }
            }
            return true;
        }

        long llMod(long a, long b, long mod) {
            return (a * b - (long) ((double) a / mod * b + 0.5) * mod + mod) % mod;
//        long r = 0;
//        a %= mod;
//        b %= mod;
//        while (b > 0) {
//            if ((b & 1) == 1) {
//                r = (r + a) % mod;
//            }
//            b >>= 1;
//            a = (a << 1) % mod;
//        }
//        return r;
        }

        long pow(long a, long n) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = ans * a;
                }
                a = a * a;
                n >>= 1;
            }
            return ans;
        }

        long pow(long a, long n, long mod) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = llMod(ans, a, mod);
                }
                a = llMod(a, a, mod);
                n >>= 1;
            }
            return ans;
        }

        private long[][] initC(int n) {
            long c[][] = new long[n][n];

            for (int i = 0; i < n; i++) {
                c[i][0] = 1;
            }

            for (int i = 1; i < n; i++) {
                for (int j = 1; j <= i; j++) {
                    c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
                }
            }
            return c;
        }

        /**
         * ps: n >= m, choose m from n;
         */
        private int cmn(long n, long m) {
            if (m > n) {
                n ^= m;
                m ^= n;
                n ^= m;
            }
            m = Math.min(m, n - m);

            long top = 1;
            long bot = 1;
            for (long i = n - m + 1; i <= n; i++) {
                top = (top * i) % MOD;
            }
            for (int i = 1; i <= m; i++) {
                bot = (bot * i) % MOD;
            }

            return (int) ((top * pow(bot, MOD - 2, MOD)) % MOD);
        }

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

        boolean isEven(long n) {
            return (n & 1) == 0;
        }

        interface BinSearch {
            boolean binSearchCmp(long k);
        }
    }

    private static class InOut {
        private BufferedReader br;
        private StreamTokenizer st;
        private PrintWriter pw;

        InOut() {
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StreamTokenizer(br);
            pw = new PrintWriter(new OutputStreamWriter(System.out));
            st.ordinaryChar('\'');
            st.ordinaryChar('\"');
            st.ordinaryChar('/');
        }

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

        private String next(int len) throws IOException {
            char ch[] = new char[len];
            int cur = 0;
            char c;
            while ((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t') ;
            do {
                ch[cur++] = c;
            } while (!((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t'));
            return String.valueOf(ch, 0, cur);
        }

        private int nextInt() throws IOException {
            st.nextToken();
            return (int) st.nval;
        }

        private long nextLong(int n) throws IOException {
            return Long.parseLong(next(n));
        }

        private double nextDouble() throws IOException {
            st.nextToken();
            return st.nval;
        }

        private String[] nextSS(String reg) throws IOException {
            return br.readLine().split(reg);
        }

        private String nextLine() throws IOException {
            return br.readLine();
        }

        private void print(String s, boolean newLine) {
            if (null != s) {
                pw.print(s);
            }
            if (newLine) {
                pw.println();
            }
        }

        private void format(String format, Object... obj) {
            pw.format(format, obj);
        }

        private void flush() {
            pw.flush();
        }
    }
}