#include<bits/stdc++.h>
using namespace std;
namespace mine
{
    typedef long long ll;
    #define pr pair<int,int>
    #define FR first
    #define SE second
    #define MP make_pair
    #define PB push_back
    #define vc vector
    #define all(x) (x).begin(),(x).end()
    #define sz(x) ((int)(x).size())
    #define bin(x) (1ll<<(x))
    #define GG(x) if(x) puts("error")
    #define rep(i,l,r) for(int i=(l);i<=(r);i++)
    ll qread()
    {
        ll ans=0,f=1;char c=getchar();
        while(c<'0' or c>'9') {if(c=='-')f=-1;c=getchar();}
        while('0'<=c and c<='9') ans=ans*10+c-'0',c=getchar();
        return ans*f;
    }
    void write(ll num)
    {
        if(num<0) putchar('-'),num=-num;
        if(num>=10) write(num/10);
        putchar('0'+num%10);
    }
    void write1(ll num){write(num);putchar(' ');}
    void write2(ll num){write(num);putchar('\n');}
    template<typename T> void chmax(T &x,const T y) {x=(x>y?x:y);}
    template<typename T> void chmin(T &x,const T y) {x=(x<y?x:y);}
    ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}

    const int INF=0x3f3f3f3f;
    const int MOD=1e9+7;
    inline int mm(const int x){return x>=MOD?x-MOD:x;}
    template<typename T> inline void add(T &x,const T y){x=mm(x+y);}
    inline ll qpower(ll x,ll e)
    {
        ll ans=1;GG(e<0);
        while(e){if(e&1)ans=ans*x%MOD;x=x*x%MOD;e>>=1;}return ans;
    }
    ll invm(ll x){return qpower(x,MOD-2);}
    const int N=3e3+10;

    vc<int> to[N];ll f[N][N],s[N][N];int n,D;
    void dp(int x,int fa)
    {
        rep(i,1,n+1) f[x][i]=1;
        rep(t,0,sz(to[x])-1)
        {
            int y=to[x][t];if(y==fa) continue;dp(y,x);
            rep(i,1,n+1) f[x][i]=f[x][i]*s[y][i]%MOD;
        }
        rep(i,1,n+1) s[x][i]=mm(s[x][i-1]+f[x][i]);
    }
    ll g[N],C[N][N];
    void main()
    {
        C[0][0]=1;rep(i,1,n){C[i][0]=1;rep(j,1,i) C[i][j]=mm(C[i-1][j-1]+C[i-1][j]);}

        n=qread(),D=qread();rep(i,2,n) to[qread()].PB(i);dp(1,0);
        ll ans=0;
        rep(i,1,n+1)
        {
            ll a=1,b=1;rep(j,1,n+1) if(i!=j) a=a*(MOD+D-j)%MOD,b=b*(MOD+i-j)%MOD;
            add(ans, a*invm(b)%MOD*s[1][i]%MOD );
        }
        write(ans);
    }//(ans+MOD)%MOD
};
int main()
{
    srand(time(0));
    mine::main();
}