#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set 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 (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } MDCONST ModInt() : val_(0) {} MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val_ != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val_); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val_ + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val_ % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv().val() % md); } MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; } MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; } MDCONST bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST ModInt inv() const { if (this->val_ < std::min(md >> 1, 1 << 21)) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } MDCONST ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } MDCONST ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } MDCONST ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; #include #include #include struct ModIntRuntime { private: static int md; public: using lint = long long; static int mod() { return md; } int val_; static std::vector &facs() { static std::vector facs_; return facs_; } static int &get_primitive_root() { static int primitive_root_ = 0; if (!primitive_root_) { primitive_root_ = [&]() { std::set 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; } int val() const noexcept { return val_; } 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().val() % 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().val() % 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 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); } ModIntRuntime inv() const { return this->pow(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; using mint = ModIntRuntime; // Calculate x^n template S pow_op(S x, long long n) { assert(n > 0); S ans = x; --n; while (n) { if (n & 1) ans = op(ans, x); x = op(x, x); n >>= 1; } return ans; } long long N, M, L, K, B; void trun(vector &vec) { while ((int)vec.size() - 1 - L >= 0) { vec.at(vec.size() - 1 - L) += vec.at(vec.size() - 1) * M; vec.pop_back(); } }; vector op(vector l, vector r) { vector ret(l.size() + r.size() - 1); REP(i, l.size()) REP(j, r.size()) ret.at(i + j) += l.at(i) * r.at(j); trun(ret); return ret; } int main() { cin >> N >> M >> L >> K >> B; mint::set_mod(B); vector trans{1, 1}; trans = pow_op(trans, N); vector init(L); init.front() += 1; auto ret = op(trans, init); trun(ret); ret.resize(L); cout << ret.at(K) << '\n'; }