#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r)-1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } int pct(int x) { return __builtin_popcount(x); } int pct(ll x) { return __builtin_popcountll(x); } int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template void reorder(vector &a, const vector &ord) { int n = a.size(); vector b(n); for (int i = 0; i < n; i++) b[i] = a[ord[i]]; swap(a, b); } template T floor(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? x / y : (x - y + 1) / y); } template T ceil(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? (x + y - 1) / y : x / y); } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; constexpr int inf = (1 << 30) - 1; constexpr ll INF = (1LL << 60) - 1; // constexpr int MOD = 1000000007; constexpr int MOD = 998244353; struct Runtime_Mod_Int { int x; Runtime_Mod_Int() : x(0) {} Runtime_Mod_Int(long long y) { x = y % get_mod(); if (x < 0) x += get_mod(); } static inline int &get_mod() { static int mod = 0; return mod; } static void set_mod(int md) { get_mod() = md; } Runtime_Mod_Int &operator+=(const Runtime_Mod_Int &p) { if ((x += p.x) >= get_mod()) x -= get_mod(); return *this; } Runtime_Mod_Int &operator-=(const Runtime_Mod_Int &p) { if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod(); return *this; } Runtime_Mod_Int &operator*=(const Runtime_Mod_Int &p) { x = (int)(1LL * x * p.x % get_mod()); return *this; } Runtime_Mod_Int &operator/=(const Runtime_Mod_Int &p) { *this *= p.inverse(); return *this; } Runtime_Mod_Int &operator++() { return *this += Runtime_Mod_Int(1); } Runtime_Mod_Int operator++(int) { Runtime_Mod_Int tmp = *this; ++*this; return tmp; } Runtime_Mod_Int &operator--() { return *this -= Runtime_Mod_Int(1); } Runtime_Mod_Int operator--(int) { Runtime_Mod_Int tmp = *this; --*this; return tmp; } Runtime_Mod_Int operator-() const { return Runtime_Mod_Int(-x); } Runtime_Mod_Int operator+(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) += p; } Runtime_Mod_Int operator-(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) -= p; } Runtime_Mod_Int operator*(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) *= p; } Runtime_Mod_Int operator/(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) /= p; } bool operator==(const Runtime_Mod_Int &p) const { return x == p.x; } bool operator!=(const Runtime_Mod_Int &p) const { return x != p.x; } Runtime_Mod_Int inverse() const { assert(*this != Runtime_Mod_Int(0)); return pow(get_mod() - 2); } Runtime_Mod_Int pow(long long k) const { Runtime_Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Runtime_Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Runtime_Mod_Int &p) { long long a; is >> a; p = Runtime_Mod_Int(a); return is; } }; using mint = Runtime_Mod_Int; template struct Matrix { vector> A; int n, m; Matrix(int n, int m) : A(n, vector(m, 0)), n(n), m(m) {} inline const vector &operator[](int k) const { return A[k]; } inline vector &operator[](int k) { return A[k]; } static Matrix I(int l) { Matrix ret(l, l); for (int i = 0; i < l; i++) ret[i][i] = 1; return ret; } Matrix &operator*=(const Matrix &B) { assert(m == B.n); Matrix ret(n, B.m); for (int i = 0; i < n; i++) { for (int k = 0; k < m; k++) { for (int j = 0; j < B.m; j++) ret[i][j] += A[i][k] * B[k][j]; } } swap(A, ret.A); m = B.m; return *this; } Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; } Matrix pow(long long k) const { assert(n == m); Matrix now = *this, ret = I(n); for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } bool eq(const T &a, const T &b) const { return a == b; // return abs(a-b) <= EPS; } // 行基本変形を用いて簡約化を行い、(rank, det) の組を返す pair row_reduction(vector &b) { assert((int)b.size() == n); if (n == 0) return make_pair(0, m > 0 ? 0 : 1); int check = 0, rank = 0; T det = (n == m ? 1 : 0); for (int j = 0; j < m; j++) { int pivot = check; for (int i = check; i < n; i++) { if (A[i][j] != 0) pivot = i; // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら } if (check != pivot) det *= T(-1); swap(A[check], A[pivot]), swap(b[check], b[pivot]); if (eq(A[check][j], T(0))) { det = T(0); continue; } rank++; det *= A[check][j]; T r = T(1) / A[check][j]; for (int k = j + 1; k < m; k++) A[check][k] *= r; b[check] *= r; A[check][j] = T(1); for (int i = 0; i < n; i++) { if (i == check) continue; if (!eq(A[i][j], 0)) { for (int k = j + 1; k < m; k++) A[i][k] -= A[i][j] * A[check][k]; b[i] -= A[i][j] * b[check]; } A[i][j] = T(0); } if (++check == n) break; } return make_pair(rank, det); } pair row_reduction() { vector b(n, T(0)); return row_reduction(b); } // 行基本変形を行い、逆行列を求める pair inverse() { if (n != m) return make_pair(false, Matrix(0, 0)); if (n == 0) return make_pair(true, Matrix(0, 0)); Matrix ret = I(n); for (int j = 0; j < n; j++) { int pivot = j; for (int i = j; i < n; i++) { if (A[i][j] != 0) pivot = i; // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら } swap(A[j], A[pivot]), swap(ret[j], ret[pivot]); if (eq(A[j][j], T(0))) return make_pair(false, Matrix(0, 0)); T r = T(1) / A[j][j]; for (int k = j + 1; k < n; k++) A[j][k] *= r; for (int k = 0; k < n; k++) ret[j][k] *= r; A[j][j] = T(1); for (int i = 0; i < n; i++) { if (i == j) continue; if (!eq(A[i][j], T(0))) { for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k]; for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k]; } A[i][j] = T(0); } } return make_pair(true, ret); } // Ax = b の解の 1 つと解空間の基底の組を返す vector> Gaussian_elimination(vector b) { row_reduction(b); vector> ret; vector p(n, m); vector is_zero(m, true); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { if (!eq(A[i][j], T(0))) { p[i] = j; break; } } if (p[i] < m) { is_zero[p[i]] = false; } else if (!eq(b[i], T(0))) { return {}; } } vector x(m, T(0)); for (int i = 0; i < n; i++) { if (p[i] < m) x[p[i]] = b[i]; } ret.push_back(x); for (int j = 0; j < m; j++) { if (!is_zero[j]) continue; x[j] = T(1); for (int i = 0; i < n; i++) { if (p[i] < m) x[p[i]] = -A[i][j]; } ret.push_back(x); x[j] = T(0); } return ret; } }; template vector Berlekamp_Massey(const vector &a) { int n = a.size(); vector c = {-1}, c_pre = {0}; int i_pre = -1; T x_pre = 1; for (int i = 0; i < n; i++) { int d = c.size(), d_pre = c_pre.size(); T x = 0; for (int j = 0; j < d; j++) x += a[i - j] * c[j]; if (x == 0) continue; T coef = -x / x_pre; if (d >= d_pre + i - i_pre) { for (int j = 0; j < d_pre; j++) c[i - i_pre + j] += coef * c_pre[j]; } else { vector memo = c; c.resize(d_pre + i - i_pre); for (int j = 0; j < d_pre; j++) { c[i - i_pre + j] += coef * c_pre[j]; } c_pre = memo, i_pre = i, x_pre = x; } } return c; } template struct Kitamasa { // d 項間線形漸化式 a[n] = c[1]*a[n-1]+c[2]*a[n-2]+...+c[d]*a[n-d] const vector a, c; const int d; // f(x) := x^d-c[1]*x^(d-1)-...-c[d-1]*x-c[d] vector f; Kitamasa(const vector &a, const vector &c) : a(a), c(c), d(a.size()) { f.resize(d + 1); f[d] = 1; for (int i = 1; i <= d; i++) f[d - i] = -c[i]; } // p(x)*q(x) を f(x) で割った余り vector mul(const vector &p, const vector &q) const { int n = p.size(), m = q.size(); vector ret(n + m - 1, 0); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) ret[i + j] += p[i] * q[j]; } for (int i = n + m - 2; i >= d; i--) { for (int j = 1; j <= d; j++) ret[i - j] -= ret[i] * f[d - j]; } ret.resize(d); return ret; } // p(x)^n を f(x) で割った余り vector pow(vector p, long long n) const { vector ret(1, 0); ret[0] = 1; while (n) { if (n & 1) ret = mul(ret, p); p = mul(p, p), n >>= 1; } return ret; } // a[n] (0-indexed) T operator[](long long n) const { if (n < d) return a[n]; vector x(d + 1, 0); x[1] = 1, x = pow(x, n); T ret = 0; for (int i = 0; i < d; i++) ret += x[i] * a[i]; return ret; } }; void solve() { ll N, M, L, K, B; cin >> N >> M >> L >> K >> B; if (M % B == 0) { cout << "0\n"; return; } mint::set_mod(B); auto mul = [&](vector x) { vector y(L, 0); y[0] = x[0] + x[L - 1] * mint(M); rep2(i, 1, L) y[i] = x[i - 1] + x[i]; return y; }; vector comb(L + 1, vector(L + 1, mint(0))); comb[0][0] = 1; rep(i, L) { rep(j, i + 1) { comb[i + 1][j] += comb[i][j]; comb[i + 1][j + 1] += comb[i][j]; } } vector a(L); vector x(L, 0); x[0] = 1; rep(i, L) { a[i] = x[K]; x = mul(x); } vector c(L + 1, 0); rep2(i, 1, L + 1) c[i] = comb[L][i] * (L & 1 ? 1 : -1); c[L] += (L & 1 ? -M : M); // vector c = Berlekamp_Massey(a); // print(a), print(c); Kitamasa lr(a, c); cout << lr[N] << '\n'; } int main() { int T = 1; // cin >> T; while (T--) solve(); }