382_E. Ksenia and Combinatorics_13606
Ksenia has her winter exams. Today she is learning combinatorics. Here's one of the problems she needs to learn to solve.

How many distinct trees are there consisting of n vertices, each with the following properties:

  * the tree is marked, that is, the vertices of the tree are numbered from 1 to n; 
  * each vertex of the tree is connected with at most three other vertices, and at the same moment the vertex with number 1 is connected with at most two other vertices; 
  * the size of the tree's maximum matching equals k. 



Two trees are considered distinct if there are such two vertices u and v, that in one tree they are connected by an edge and in the other tree they are not.

Help Ksenia solve the problem for the given n and k. As the answer to the problem can be very huge you should output it modulo 1000000007 (109 + 7).

Input

The first line contains two integers n, k (1 ≤ n, k ≤ 50).

Output

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

1 1


Output

0


Input

2 1


Output

1


Input

3 1


Output

3


Input

4 2


Output

12

Note

If you aren't familiar with matchings, please, read the following link: http://en.wikipedia.org/wiki/Matching_(graph_theory).
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.List;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.InputStream;

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

class TaskE {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n=in.readInt(), k=in.readInt(), MOD=1000000007;
        long[][] C= IntegerUtils.generateBinomialCoefficients(n+1, MOD);
        long[][][]dp=new long[n+1][k+1][2];
        dp[0][0][1]=dp[1][0][0]=1;
        for (int i=2; i<=n; i++) for (int j=0; j<=k; j++) for (int l=1; l<i; l++) {
            long aux=C[i-2][l-1]*MiscUtils.max(1, l)%MOD* MiscUtils.max(i - l - 1, 1)%MOD;
            for (int m=0; m<=j; m++) {
                dp[i][j][0]=(dp[i][j][0]+dp[l][m][1]*dp[i-l-1][j-m][1]%MOD*aux%MOD)%MOD;
                dp[i][j][1]=(dp[i][j][1]+dp[l][m][0]*(j>m?dp[i-l-1][j-m-1][0]+dp[i-l-1][j-m-1][1]:0)%MOD*aux%MOD+dp[l][m][1]*(j>m?dp[i-l-1][j-m-1][0]:0)%MOD*aux%MOD)%MOD;
            }
        }
        //debug(out, dp);
        out.printLine((dp[n][k][0]+dp[n][k][1])%MOD);
    }

}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

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

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void close() {
        writer.close();
    }

    public void printLine(long i) {
        writer.println(i);
    }

}

class IntegerUtils {

    public static long[][] generateBinomialCoefficients(int n, long module) {
        long[][] result = new long[n + 1][n + 1];
        if (module == 1)
            return result;
        for (int i = 0; i <= n; i++) {
            result[i][0] = 1;
            for (int j = 1; j <= i; j++) {
                result[i][j] = result[i - 1][j - 1] + result[i - 1][j];
                if (result[i][j] >= module)
                    result[i][j] -= module;
            }
        }
        return result;
    }

}

class MiscUtils {

    public static<T extends Comparable<T>> T max(T first, T second) {
        if (first.compareTo(second) <= 0)
            return second;
        return first;
    }

}
