#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=87;
const int ha=1000000007;
int n,k,a[maxn][maxn];
int fa,b[maxn][maxn];
int c[maxn][maxn],ans;inline int add(int x,int y){x+=y;return x>=ha?x-ha:x;
}inline int ksm(int x,int y){int an=1;for(;y;y>>=1,x=x*(ll)x%ha) if(y&1) an=an*(ll)x%ha;return an;
}inline int matrix_tree(int x){int an=1;memset(b,0,sizeof(b));for(int i=1;i<=n;i++)for(int j=i+1;j<=n;j++){if(a[i][j]) b[i][j]=b[j][i]=ha-1,b[i][i]++,b[j][j]++;else b[i][j]=b[j][i]=ha-x,b[i][i]+=x,b[j][j]+=x;}for(int i=1;i<n;i++){int tmp=i;for(;tmp<n;tmp++) if(b[tmp][i]) break;if(tmp>i){an=ha-an;for(int k=i;k<n;k++) swap(b[i][k],b[tmp][k]);}for(int j=i+1;j<n;j++)while(b[j][i]){an=ha-an;int A=b[i][i]/b[j][i];for(int k=i;k<n;k++){b[i][k]=((ll)b[i][k]-b[j][k]*(ll)A)%ha;if(b[i][k]<0) b[i][k]+=ha;swap(b[i][k],b[j][k]);}}an=an*(ll)b[i][i]%ha;}return an;
}inline void xy(){n++;for(int i=1;i<n;i++){if(!c[i][i]){for(int j=i+1;j<n;j++) if(c[j][i]){for(int k=i;k<=n;k++) swap(c[j][k],c[i][k]);break;}}for(int j=i+1;j<n;j++)while(c[j][i]){int A=c[i][i]/c[j][i];for(int k=i;k<=n;k++){c[i][k]=((ll)c[i][k]-c[j][k]*(ll)A)%ha;if(c[i][k]<0) c[i][k]+=ha;swap(c[i][k],c[j][k]);}}}for(int i=n-1;i;i--){for(int j=n-1;j>i;j--) c[i][n]=add(c[i][n],add(ha,-c[j][n]*(ll)c[i][j]%ha));c[i][n]=c[i][n]*(ll)ksm(c[i][i],ha-2)%ha;}
}int main(){freopen("tree.in","r",stdin);freopen("tree.out","w",stdout);scanf("%d%d",&n,&k);for(int i=2;i<=n;i++){scanf("%d",&fa);fa++,a[i][fa]++,a[fa][i]++;}for(int i=1;i<=n;i++){for(int j=1,u=1;j<=n;j++,u=u*(ll)i%ha) c[i][j]=u;c[i][n+1]=matrix_tree(i);}xy();k++;for(int i=1;i<=k;i++) ans=add(ans,c[i][n]);printf("%d\n",ans);return 0;
}