Let c_1, c_2, …, c_n be a permutation of integers 1, 2, …, n. Consider all subsegments of this permutation containing an integer x. Given an integer m, we call the integer x good if there are exactly m different values of maximum on these subsegments.

Cirno is studying mathematics, and the teacher asks her to count the number of permutations of length n with exactly k good numbers.

Unfortunately, Cirno isn't good at mathematics, and she can't answer this question. Therefore, she asks you for help.

Since the answer may be very big, you only need to tell her the number of permutations modulo p.

A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

A sequence a is a subsegment of a sequence b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

The first line contains four integers n, m, k, p (1 ≤ n ≤ 100, 1 ≤ m ≤ n, 1 ≤ k ≤ n, 1 ≤ p ≤ 10^9).

Output

Output the number of permutations modulo p.

Examples

Input


4 3 2 10007


Output


4


Input


6 4 1 769626776


Output


472


Input


66 11 9 786747482


Output


206331312


Input


99 30 18 650457567


Output


77365367

Note

In the first test case, there are four permutations: [1, 3, 2, 4], [2, 3, 1, 4], [4, 1, 3, 2] and [4, 2, 3, 1].

Take permutation [1, 3, 2, 4] as an example:

For number 1, all subsegments containing it are: [1], [1, 3], [1, 3, 2] and [1, 3, 2, 4], and there're three different maxima 1, 3 and 4.

Similarly, for number 3, there're two different maxima 3 and 4. For number 2, there're three different maxima 2, 3 and 4. And for number 4, there're only one, that is 4 itself.
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

struct ModIntRuntime {
private:
    static int md;

public:
    using lint = long long;
    static int mod() { return md; }
    int val;
    static std::vector<ModIntRuntime> &facs() {
        static std::vector<ModIntRuntime> facs_;
        return facs_;
    }
    static int &get_primitive_root() {
        static int primitive_root_ = 0;
        if (!primitive_root_) {
            primitive_root_ = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModIntRuntime(g).power((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root_;
    }
    static void set_mod(const int &m) {
        if (md != m) facs().clear();
        md = m;
        get_primitive_root() = 0;
    }
    ModIntRuntime &_setval(lint v) {
        val = (v >= md ? v - md : v);
        return *this;
    }
    ModIntRuntime() : val(0) {}
    ModIntRuntime(lint v) { _setval(v % md + md); }
    explicit operator bool() const { return val != 0; }
    ModIntRuntime operator+(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val + x.val);
    }
    ModIntRuntime operator-(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val - x.val + md);
    }
    ModIntRuntime operator*(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val * x.val % md);
    }
    ModIntRuntime operator/(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val * x.inv() % md);
    }
    ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val); }
    ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
    ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
    ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
    ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
    friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md + x.val);
    }
    friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md - x.val + md);
    }
    friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.val % md);
    }
    friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.inv() % md);
    }
    bool operator==(const ModIntRuntime &x) const { return val == x.val; }
    bool operator!=(const ModIntRuntime &x) const { return val != x.val; }
    bool operator<(const ModIntRuntime &x) const { return val < x.val; } // To use std::map<ModIntRuntime, T>
    friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {
        lint t;
        return is >> t, x = ModIntRuntime(t), is;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) { return os << x.val; }

    lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % md;
            tmp = tmp * tmp % md;
            n /= 2;
        }
        return ans;
    }
    ModIntRuntime pow(lint n) const { return power(n); }
    lint inv() const { return this->power(md - 2); }

    ModIntRuntime fac() const {
        int l0 = facs().size();
        if (l0 > this->val) return facs()[this->val];

        facs().resize(this->val + 1);
        for (int i = l0; i <= this->val; i++)
            facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
        return facs()[this->val];
    }

    ModIntRuntime doublefac() const {
        lint k = (this->val + 1) / 2;
        return (this->val & 1) ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
                               : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
    }

    ModIntRuntime nCr(const ModIntRuntime &r) const {
        return (this->val < r.val) ? ModIntRuntime(0) : this->fac() / ((*this - r).fac() * r.fac());
    }

    ModIntRuntime sqrt() const {
        if (val == 0) return 0;
        if (md == 2) return val;
        if (power((md - 1) / 2) != 1) return 0;
        ModIntRuntime b = 1;
        while (b.power((md - 1) / 2) == 1) b += 1;
        int e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModIntRuntime z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModIntRuntime t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModIntRuntime(std::min(x.val, md - x.val));
    }
};
int ModIntRuntime::md = 1;


int main() {
    auto START = std::chrono::system_clock::now();
    int N, M, K, P;
    cin >> N >> M >> K >> P;
    if (M + K > N + 2) {
        puts("0");
        return 0;
    }
    using mint = ModIntRuntime;
    mint::set_mod(P);
    vector ncr(500, vector<mint>(500));
    REP(i, ncr.size()) ncr[i][0] = 1;
    FOR(i, 1, ncr.size()) FOR(j, 1, ncr[i].size()) {
        ncr[i][j] = ncr[i - 1][j - 1] + ncr[i - 1][j];
    }

    vector<mint> fac(201, 1);
    FOR(i, 1, fac.size()) fac[i] = fac[i - 1] * i;

    vector dp(N + 1, vector(M + 1, vector<mint>(K + 1)));

    REP(l, M + 1) dp[1][l][0] = (l != 1);
    dp[1][1][1] = 1;

    REP(l, M + 1) dp[0][l][0] = 1;

    FOR(l, 1, M + 1) FOR(n, 2, N + 1) REP(k, K + 1) {
        int64_t spent_ms = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count();
        if (spent_ms > 1800) {
            puts("0");
            return 0;
        }
        if (l == 1) {
            if (k == 1) dp[n][l][k] = fac[n];
        } else {
            REP(i, n) REP(kk, k + 1) {
                dp[n][l][k] += dp[i][l - 1][kk] * dp[n - 1 - i][l - 1][k - kk] * ncr[n - 1][i];
            }
        }
    }
    cout << dp[N][M][K] << '\n';
}
