#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


int N, K;
vector<int> P;

vector<vector<int>> graph;


namespace brute {
vector<int> ls;
void dfs(int u) {
  if (!graph[u].empty()) {
    for (const int v : graph[u]) {
      dfs(v);
    }
  } else {
    ls.push_back(u);
  }
}
bool adj[20][20];
void ae(int u, int v) {
  adj[u][v] = adj[v][u] = true;
}
Mint dp[1 << 19][20];
Mint run() {
  if (N <= 2) {
    return 0;
  }
  ls.clear();
  dfs(0);
  memset(adj, 0, sizeof(adj));
  for (int u = 1; u < N; ++u) {
    ae(P[u], u);
  }
  const int lsLen = ls.size();
  for (int j = 0; j < lsLen; ++j) for (int k = 1; k <= K; ++k) {
    ae(ls[j], ls[(j + k) % lsLen]);
  }
  memset(dp, 0, sizeof(dp));
  dp[0][N - 1] = 1;
  for (int p = 0; p < 1 << (N - 1); ++p) {
    for (int u = 0; u < N; ++u) if (dp[p][u]) {
      for (int v = 0; v < N - 1; ++v) if (!(p & 1 << v) && adj[u][v]) {
        dp[p | 1 << v][v] += dp[p][u];
      }
    }
  }
  Mint ans = 0;
  for (int u = 0; u < N; ++u) if (adj[N - 1][u]) {
    ans += dp[(1 << (N - 1)) - 1][u];
  }
  ans /= 2;
  return ans;
}
}  // brute


namespace k1 {
vector<int> ls;
vector<Mint> UL, UR, LR;
Mint ans;
void dfs(int u) {
  const int deg = graph[u].size();
  if (deg) {
    for (const int v : graph[u]) {
      dfs(v);
    }
    vector<Mint> pre(deg + 1), suf(deg + 1);
    pre[0] = 1;
    for (int j = 0; j < deg; ++j) pre[j + 1] = pre[j] * LR[graph[u][j]];
    suf[deg] = 1;
    for (int j = deg; --j >= 0; ) suf[j] = LR[graph[u][j]] * suf[j + 1];
    UL[u] = pre[deg - 1] * UL[graph[u][deg - 1]];
    UR[u] = UR[graph[u][0]] * suf[1];
    for (int j = 0; j < deg - 1; ++j) {
      LR[u] += pre[j] * UL[graph[u][j]] * UR[graph[u][j + 1]] * suf[j + 2];
    }
    if (u == 0 && deg >= 2) {
      ans += LR[0];
      if (ls.size() >= 3) {
        Mint prod = 1;
        prod *= UR[graph[u][0]];
        for (int j = 1; j < deg - 1; ++j) prod *= LR[graph[u][j]];
        prod *= UL[graph[u][deg - 1]];
        ans += prod;
      }
    }
  } else {
    ls.push_back(u);
    UL[u] = UR[u] = LR[u] = 1;
  }
}
Mint run() {
  ls.clear();
  UL.assign(N, 0);
  UR.assign(N, 0);
  LR.assign(N, 0);
  ans = 0;
  dfs(0);
  return ans;
}
}  // k1


int main() {
  for (; ~scanf("%d%d", &N, &K); ) {
    P.assign(N, -1);
    for (int u = 1; u < N; ++u) {
      scanf("%d", &P[u]);
      --P[u];
    }
    
    graph.assign(N, {});
    for (int u = 1; u < N; ++u) {
      graph[P[u]].push_back(u);
    }
    
    Mint ans = 0;
    if (K == 1) {
      ans = k1::run();
    } else if (N <= 20) {
      ans = brute::run();
    }
    printf("%u\n", ans.x);
#ifdef LOCAL
if(N<=20){
 const Mint brt=brute::run();
 if(brt!=ans)cerr<<N<<" "<<K<<" "<<P<<": "<<brt<<" "<<ans<<endl;
 assert(brt==ans);
}
#endif
  }
  return 0;
}