Allen, having graduated from the MOO Institute of Techcowlogy (MIT), has started a startup! Allen is the president of his startup. He also hires n-1 other employees, each of which is assigned a direct superior. If u is a superior of v and v is a superior of w then also u is a superior of w. Additionally, there are no u and v such that u is the superior of v and v is the superior of u. Allen himself has no superior. Allen is employee number 1, and the others are employee numbers 2 through n.

Finally, Allen must assign salaries to each employee in the company including himself. Due to budget constraints, each employee's salary is an integer between 1 and D. Additionally, no employee can make strictly more than his superior.

Help Allen find the number of ways to assign salaries. As this number may be large, output it modulo 10^9 + 7.

Input

The first line of the input contains two integers n and D (1 ≤ n ≤ 3000, 1 ≤ D ≤ 10^9).

The remaining n-1 lines each contain a single positive integer, where the i-th line contains the integer p_i (1 ≤ p_i ≤ i). p_i denotes the direct superior of employee i+1.

Output

Output a single integer: the number of ways to assign salaries modulo 10^9 + 7.

Examples

Input

3 2
1
1


Output

5


Input

3 3
1
2


Output

10


Input

2 5
1


Output

15

Note

In the first sample case, employee 2 and 3 report directly to Allen. The three salaries, in order, can be (1,1,1), (2,1,1), (2,1,2), (2,2,1) or (2,2,2).

In the second sample case, employee 2 reports to Allen and employee 3 reports to employee 2. In order, the possible salaries are (1,1,1), (2,1,1), (2,2,1), (2,2,2), (3,1,1), (3,2,1), (3,2,2), (3,3,1), (3,3,2), (3,3,3).
import java.util.*;
import java.io.*;

public class F
{

    static int mod = (int) (1e9 + 7);
    static InputReader in;
    static PrintWriter out;
    static long[][] dp;
    static ArrayList<Integer>[] g;
    static int n;
    
    static void dfs(int u) {
        
        for(int v: g[u]) {
            dfs(v);
        }
        
        for(int i = 1; i <= n; i++) {
            long tmp = 1;
            for(int v: g[u]) {
                tmp = mul(tmp, dp[v][i]);
            }
            dp[u][i] = add(dp[u][i - 1], tmp);
        }
//        debug(u,dp[u]);
    }
    
    public static void main(String[] args)
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        n = in.nextInt();
        int d = in.nextInt();
        
        dp = new long[n + 1][n + 1];
        g = new ArrayList[n + 1];
        for(int i = 1; i <= n; i++)
            g[i] = new ArrayList<>();
        
        for(int i = 2; i <= n; i++) {
            int b = in.nextInt();
            g[b].add(i);
        }
        dfs(1);
        long[][] nCr = new long[n + 1][n + 1];
        
        for(int i = 0; i <= n; i++)
            nCr[i][0] = 1;
        
        for(int i = 1; i <= n; i++) {
            for(int j = 1; j <= i; j++)
                nCr[i][j] = add(nCr[i - 1][j], nCr[i - 1][j - 1]);
        }
        
        long[] dp0 = new long[n + 1];
        long res = 0;
        if(d < n) res = dp[1][d];
        else {
            for(int i = 1; i <= n; i++) {
                long tmp = 0;
                for(int j = 1; j < i; j++) {
                    tmp = add(tmp, mul(dp0[j], nCr[i][j]));
                }
                dp0[i] = sub(dp[1][i], tmp);
                long a = 1;
                for(int j = d; j > d - i; j--)
                    a = mul(a, j);
                long b = 1;
                for(int j = 1; j <= i; j++)
                    b = mul(b, j);
//                debug(i,tmp,dp0[i],a,b);
                res = add(res, mul(dp0[i], mul(a, pow(b, mod - 2, mod))));
            }
        }
        
        out.println(res);
        out.close();
    }

    static long add(long a, long b) {
        return (a + b) % mod;
    }
    
    static long mul(long a, long b) {
        return (a * b) % mod;
    }
    
    static long sub(long a, long b) {
        return (a - b + mod) % mod;
    } 
    
    static class Pair implements Comparable<Pair>
    {

        int x,y;
        int i;

        Pair (int x,int y)
        {
                this.x = x;
                this.y = y;
        }

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

        public int compareTo(Pair o)
        {
                return 0;
        }

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y + " "+i;
        }

        /*public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }*/

    } 

    static String rev(String s){
        StringBuilder sb=new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }

    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0){
            return 1;
          }

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result >= m)
               result %= m;
            p >>=1;
            n*=n;
            if(n >= m)
                n%=m;
        }

        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

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

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

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

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

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

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

        public int[] nextIntArray(int n)
        {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextInt();
                }
                return a;
        }

        public long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                return a;
        }

        public String readString()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

        public String nextLine()
        {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }

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

    }
}    