You are given an undirected graph without self-loops or multiple edges which consists of n vertices and m edges. Also you are given three integers n_1, n_2 and n_3.

Can you label each vertex with one of three numbers 1, 2 or 3 in such way, that: 

  1. Each vertex should be labeled by exactly one number 1, 2 or 3; 
  2. The total number of vertices with label 1 should be equal to n_1; 
  3. The total number of vertices with label 2 should be equal to n_2; 
  4. The total number of vertices with label 3 should be equal to n_3; 
  5. |col_u - col_v| = 1 for each edge (u, v), where col_x is the label of vertex x. 



If there are multiple valid labelings, print any of them.

Input

The first line contains two integers n and m (1 ≤ n ≤ 5000; 0 ≤ m ≤ 10^5) — the number of vertices and edges in the graph.

The second line contains three integers n_1, n_2 and n_3 (0 ≤ n_1, n_2, n_3 ≤ n) — the number of labels 1, 2 and 3, respectively. It's guaranteed that n_1 + n_2 + n_3 = n.

Next m lines contan description of edges: the i-th line contains two integers u_i, v_i (1 ≤ u_i, v_i ≤ n; u_i ≠ v_i) — the vertices the i-th edge connects. It's guaranteed that the graph doesn't contain self-loops or multiple edges.

Output

If valid labeling exists then print "YES" (without quotes) in the first line. In the second line print string of length n consisting of 1, 2 and 3. The i-th letter should be equal to the label of the i-th vertex.

If there is no valid labeling, print "NO" (without quotes).

Examples

Input


6 3
2 2 2
3 1
5 4
2 5


Output


YES
112323


Input


5 9
0 2 3
1 2
1 3
1 5
2 3
2 4
2 5
3 4
3 5
4 5


Output


NO
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author dauom
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    EGraphColoring solver = new EGraphColoring();
    solver.solve(1, in, out);
    out.close();
  }

  static class EGraphColoring {
    public final void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int m = in.nextInt();
      int n1 = in.nextInt();
      int n2 = in.nextInt();
      int n3 = in.nextInt();

      int[][] e = in.nextIntMatrix(m, 2);
      int[][] g = GraphUtils.packUndirectedUnweighted(e, n);

      int[] color = new int[n + 1];
      Arrays.fill(color, -1);
      ArrayList<EGraphColoring.Report> a = new ArrayList<>();
      for (int i = 1; i <= n; i++) {
        if (color[i] != -1) {
          continue;
        }

        EGraphColoring.Report r = new EGraphColoring.Report();
        dfs(r, g, color, i, 1);
        if (r.bad) {
          out.println("NO");
          return;
        }
        a.add(r);
      }

      EGraphColoring.Report[] r = a.toArray(new EGraphColoring.Report[0]);
      boolean[][] dp = new boolean[r.length + 1][n2 + 1];
      dp[r.length][0] = dp[r.length][0] = true;
      for (int i = r.length - 1; i >= 0; i--) {
        for (int left = 0; left <= n2; left++) {
          if (left - r[i].count >= 0) {
            dp[i][left] = dp[i + 1][left - r[i].count];
            if (dp[i][left]) {
              continue;
            }
          }
          int rem = Math.abs(r[i].nodes.size() - r[i].count);
          if (left - rem >= 0) {
            dp[i][left] = dp[i + 1][left - rem];
          }
        }
      }

      if (!dp[0][n2] && !dp[0][n2]) {
        out.println("NO");
        return;
      }

      out.println("YES");
      for (int i = 0; i < r.length; i++) {
        int rem = Math.abs(r[i].nodes.size() - r[i].count);
        if (n2 - rem >= 0 && dp[i + 1][n2 - rem]) {
          for (int u : r[i].nodes) {
            color[u] ^= 1;
          }
          n2 -= r[i].nodes.size() - r[i].count;
        } else {
          n2 -= r[i].count;
        }
        for (int u : r[i].nodes) {
          ++color[u];
          if (color[u] == 1 && n3 > 0) {
            --n3;
            color[u] = 3;
          }
        }
      }
      out.println(StringUtils.joinRange("", 1, n, color));
    }

    private void dfs(EGraphColoring.Report r, int[][] g, int[] color, int u, int c) {
      r.count += c;
      r.nodes.add(u);
      color[u] = c;
      for (int v : g[u]) {
        if (color[v] == -1) {
          dfs(r, g, color, v, c ^ 1);
          if (r.bad) {
            return;
          }
        } else if (color[v] == c) {
          r.bad = true;
          return;
        }
      }
    }

    private static final class Report {
      ArrayList<Integer> nodes = new ArrayList<>();
      boolean bad = false;
      int count = 0;
    }
  }

  static final class GraphUtils {
    private GraphUtils() {
      throw new RuntimeException("DON'T");
    }

    public static final int[][] packUndirectedUnweighted(int[][] edges, int n) {
      int[][] g = new int[n + 1][];
      int[] size = new int[n + 1];
      for (int[] edge : edges) {
        ++size[edge[0]];
        ++size[edge[1]];
      }
      for (int i = 0; i <= n; i++) {
        g[i] = new int[size[i]];
      }
      for (int[] edge : edges) {
        g[edge[0]][--size[edge[0]]] = edge[1];
        g[edge[1]][--size[edge[1]]] = edge[0];
      }
      return g;
    }
  }

  static class StringUtils {
    private StringUtils() {
      throw new RuntimeException("DON'T");
    }

    public static final String joinRange(String delimiter, int from, int to, int[] a) {
      if (from > to) {
        return "";
      }
      StringBuilder sb = new StringBuilder();
      sb.append(a[from]);
      for (int i = from + 1; i <= to; i++) {
        sb.append(delimiter).append(a[i]);
      }
      return sb.toString();
    }
  }

  static final class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[1 << 16];
    private int curChar;
    private int numChars;

    public InputReader() {
      this.stream = System.in;
    }

    public InputReader(final InputStream stream) {
      this.stream = stream;
    }

    private final int read() {
      if (this.numChars == -1) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return -1;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public final int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {}

      byte sgn = 1;
      if (c == 45) { // 45 == '-'
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) { // 48 == '0', 57 == '9'
        res *= 10;
        res += c - 48; // 48 == '0'
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    private static final boolean isSpaceChar(final int c) {
      return c == 32 || c == 10 || c == 13 || c == 9
          || c == -1; // 32 == ' ', 10 == '\n', 13 == '\r', 9 == '\t'
    }

    public final int[][] nextIntMatrix(final int n, final int m) {
      int[][] arr = new int[n][m];
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
          arr[i][j] = nextInt();
        }
      }
      return arr;
    }
  }
}
