A tree is a connected graph without cycles.

Two trees, consisting of n vertices each, are called isomorphic if there exists a permutation p: {1, ..., n} → {1, ..., n} such that the edge (u, v) is present in the first tree if and only if the edge (pu, pv) is present in the second tree.

Vertex of the tree is called internal if its degree is greater than or equal to two.

Count the number of different non-isomorphic trees, consisting of n vertices, such that the degree of each internal vertex is exactly d. Print the answer over the given prime modulo mod.

Input

The single line of the input contains three integers n, d and mod (1 ≤ n ≤ 1000, 2 ≤ d ≤ 10, 108 ≤ mod ≤ 109) — the number of vertices in the tree, the degree of internal vertices and the prime modulo.

Output

Print the number of trees over the modulo mod.

Examples

Input

5 2 433416647


Output

1


Input

10 3 409693891


Output

2


Input

65 4 177545087


Output

910726
997 6 680633279
 989 8 990767311
 999 2 750160753
 1 4 904448911
 1000 3 750160753
 1000 6 970400047
 983 10 762763321
 106 9 434448163
 2 3 434448163
 102 4 904448911
 992 10 762763321
 2 4 434448163
 2 2 434448163
 1000 2 750160753
 1 9 837744727
 1 7 727733989
 1000 10 750160753
 2 10 904448911
 102 6 944036243
 1000 5 970400047
 180 3 434448163
 992 6 680633279
 1 8 727733989
 2 8 904448911
 1 10 837744727
 102 5 944036243
 2 5 434448163
 100 8 944036243
 104 7 434448163
 996 8 990767311
 998 5 680633279
 1000 7 970400047
 101 10 944036243
 1 6 727733989
 2 7 904448911
 998 7 930423869
 998 4 817408561
 999 3 837744727
 994 9 390528763
 2 9 904448911
 100 2 944036243
 1 2 727733989
 1000 8 750160753
 2 6 904448911
 101 4 944036243
 1 3 727733989
 995 4 817408561
 1000 9 750160753
 1 5 727733989

148277591
 976760285
 1
 1
 16572167
 0
 663665406
 1296
 1
 0
 571064998
 1
 1
 1
 1
 1
 0
 1
 748711
 0
 106622108
 451750559
 1
 1
 1
 74266477
 1
 3128
 47207
 350615945
 233182629
 0
 235
 1
 1
 167343048
 443073705
 0
 211625777
 1
 1
 1
 0
 1
 467334192
 1
 36421881
 0
 1

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)

#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rsz resize

int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 200005;
const ld PI = 4*atan((ld)1);

template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }

namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);

    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class Arg, class... Args> void re(Arg& first, Args&... rest) { 
        re(first); re(rest...); 
    }

    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T, size_t SZ> void pr(const array<T,SZ>& x);
    template<class T> void pr(const vector<T>& x);
    template<class T> void pr(const set<T>& x);
    template<class T1, class T2> void pr(const map<T1,T2>& x);

    template<class T> void pr(const T& x) { cout << x; }
    template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) { 
        pr(first); pr(rest...); 
    }

    template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
        pr("{",x.f,", ",x.s,"}"); 
    }
    template<class T> void prContain(const T& x) {
        pr("{");
        bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; // const needed for vector<bool>
        pr("}");
    }
    template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
    template<class T> void pr(const vector<T>& x) { prContain(x); }
    template<class T> void pr(const set<T>& x) { prContain(x); }
    template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
    
    void ps() { pr("\n"); }
    template<class Arg> void ps(const Arg& first) { 
        pr(first); ps(); // no space at end of line
    }
    template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) { 
        pr(first," "); ps(rest...); // print w/ spaces
    }
}

using namespace output;

namespace io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
    }
}

using namespace io;

template<class T> T invGeneral(T a, T b) {
    a %= b; if (a == 0) return b == 1 ? 0 : -1;
    T x = invGeneral(b,a); 
    return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}

template<class T> struct modular {
    T val; 
    explicit operator T() const { return val; }
    modular() { val = 0; }
    modular(const ll& v) { 
        val = (-MOD <= v && v <= MOD) ? v : v % MOD;
        if (val < 0) val += MOD;
    }
    
    friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
    friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
    friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }

    modular operator-() const { return modular(-val); }
    modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
    modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
    modular& operator*=(const modular& m) { val = (ll)val*m.val%MOD; return *this; }
    friend modular pow(modular a, ll p) {
        modular ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend modular inv(const modular& a) { 
        auto i = invGeneral(a.val,MOD); assert(i != -1);
        return i;
    } // equivalent to return exp(b,MOD-2) if MOD is prime
    modular& operator/=(const modular& m) { return (*this) *= inv(m); }
    
    friend modular operator+(modular a, const modular& b) { return a += b; }
    friend modular operator-(modular a, const modular& b) { return a -= b; }
    friend modular operator*(modular a, const modular& b) { return a *= b; }
    
    friend modular operator/(modular a, const modular& b) { return a /= b; }
};

typedef modular<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int n,d;
mi dp[1001][11][1001], in[11];

int main() {
    setIO(); re(n,d,MOD);
    FOR(i,1,11) in[i] = mi(1)/i;
    F0R(k,n+1) dp[1][0][k] = 1;
    FOR(i,2,n+1) FOR(j,1,d+1) FOR(k,1,n+1) {
    	dp[i][j][k] = dp[i][j][k-1];
    	if (k == 1) {
    		if (i == j+1) dp[i][j][k] = 1;
    	} else {
			mi ways = 1; // dp[k][d-1][k-1];
	    	FOR(t,1,j+1) if (i >= t*k) {
	    		ways *= dp[k][d-1][k-1]+t-1;
	    		ways *= in[t];
	    		mi res = dp[i-t*k][j-t][k-1];
	    		dp[i][j][k] += ways*res;
	    	}
    	}
    	// ps("HUH",i,j,k,dp[i][j][k]);
    }
    mi ans = dp[n][d][(n-1)/2];
    // ps("WUT",ans);
    if (n%2 == 0) {
    	mi tr = dp[n/2][d-1][n/2-1];
    	ans += (tr+1)*tr*in[2];
    }
    ps(ans);
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?), set tle
    * do smth instead of nothing and stay organized
*/