// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll using pii = pair; #define rep(i, n) if (const int _rep_n = n; true) for (int i = 0; i < _rep_n; i++) #define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream& os, tuple const& t) { bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; } template istream& operator>>(istream& is, tuple& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << '\n'; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template ()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); } template ()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); } template constexpr T min(set const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(set const& st) { assert(st.size()); return *prev(st.end()); } template constexpr T min(multiset const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(multiset const& st) { assert(st.size()); return *prev(st.end()); } constexpr ll max(signed x, ll y) { return max(x, y); } constexpr ll max(ll x, signed y) { return max(x, y); } constexpr ll min(signed x, ll y) { return min(x, y); } constexpr ll min(ll x, signed y) { return min(x, y); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; auto four_nbd(int n, int m) { static vector> v; return [n, m](int i, int j) { const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 }; v.clear(); rep (dir, 4) { int ni = i+dx[dir], nj = j+dy[dir]; if (0 <= ni and ni < n and 0 <= nj and nj < m) { v.emplace_back(ni, nj); } } return v; }; }; template vector iota(int n, Comp comp) { vector idx(n); iota(begin(idx), end(idx), 0); stable_sort(begin(idx), end(idx), comp); return idx; } constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector &v, vector const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template auto prefix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template auto suffix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template T pop(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_back(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop(priority_queue &a) { auto x = a.top(); a.pop(); return x; } template T pop(queue &a) { auto x = a.front(); a.pop(); return x; } template T pop_front(deque &a) { auto x = a.front(); a.pop_front(); return x; } template T pop_back(deque &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_front(set &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template T pop_back(set &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template T pop_front(multiset &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template T pop_back(multiset &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } // <<< // >>> runtime modint template class runtime_modint { using u32 = uint32_t; using i32 = int32_t; using i64 = int64_t; using M = runtime_modint; u32 x; struct barrett_mul { uint32_t mod; uint64_t inv; barrett_mul() : mod(0), inv(0) { } barrett_mul(uint32_t mod) : mod(mod), inv((uint64_t)(-1) / mod + 1) { } uint32_t operator()(uint32_t a, uint32_t b) const { __uint128_t c = uint64_t(a) * b; uint64_t q = (c * inv) >> 64; uint32_t x = c - q * mod; if (mod <= x) x += mod; return x; } }; inline static barrett_mul mul; public: static void set_mod(u32 new_mod) { mul = barrett_mul(new_mod); } static int mod() { return mul.mod; } runtime_modint(i64 x = 0) : x((assert(mod() > 0), ((x %= (u32)mod()) < 0 ? x+mod() : x))) { } i64 val() const { return x; } constexpr explicit operator i64() const { return x; } bool operator==(M const& r) const { return x == r.x; } bool operator!=(M const& r) const { return x != r.x; } M operator+() const { return *this; } M operator-() const { return M()-*this; } M& operator+=(M const& r) { i64 t = i64(x) + r.x; if (t >= mod()) t -= mod(); x = t; return *this; } M& operator-=(M const& r) { i64 t = i64(x) + mod()-r.x; if (t >= mod()) t -= mod(); x = t; return *this; } M& operator*=(M const& r) { x = mul(x, r.x); return *this; } M& operator/=(M const& r) { return *this *= r.inv(); } M operator+(M r) const { return M(*this) += r; } M operator-(M r) const { return M(*this) -= r; } M operator*(M r) const { return M(*this) *= r; } M operator/(M r) const { return M(*this) /= r; } friend M operator+(i64 x, M y) { return M(x)+y; } friend M operator-(i64 x, M y) { return M(x)-y; } friend M operator*(i64 x, M y) { return M(x)*y; } friend M operator/(i64 x, M y) { return M(x)/y; } M pow(i64 n) const { // 0^0 = 1 if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } M inv() const { uint32_t a = x, b = mod(); int64_t u = 1, v = 0; while (b) { int64_t q = a / b; swap(a -= q * b, b); swap(u -= q * v, v); } assert(a == 1); return u; } static i64 gen() { // assume mod():prime if (mod() == 2) return 1; assert(mod() >= 3); for (int i = 2; i*i <= mod(); i++) assert(mod() % i != 0); vector ps; int n = mod()-1; for (int i = 2; i*i <= n; ++i) { if (n % i) continue; ps.push_back(i); do n /= i; while (n % i == 0); } if (n > 1) ps.push_back(n); n = mod()-1; auto check = [&](M g) { for (int p : ps) if (g.pow(n/p) == 1) return false; return true; }; for (int g = 2; g <= n; ++g) if (check(g)) return g; return -1; } // return minimum k >= (allow_zero ? 0 : 1) s.t. this->pow(k) == y // return -1 if not found int log(M y, bool allow_zero = false) { if (allow_zero and pow(0) == y) return 0; auto x = *this; M z = 1; int k = 0; while ((1u << k) < mod()) { z *= x, k++; if (z == y) return k; } u32 g = gcd(z.x, mod()); if (y.x % g != 0) return -1; auto old_mul = mul; mul = barrett_mul(mod()/g); x.x %= mod(), y.x /= g, z.x /= g; unordered_map m; int s = 0; M w = 1; for ( ; s*s < mod(); s++) m[(y*w).x] = s, w *= x; while (k < mod()) { z *= w, k += s; if (m.count(z.x)) { swap(mul, old_mul); return k - m[z.x]; } } swap(mul, old_mul); return -1; } #ifdef LOCAL // friend string to_s(M r) { return to_s(r.val(), M::mod()); } friend string to_s(M r) { return to_s(r.val()); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; using mint = runtime_modint<-1>; // <<< int32_t main() { mint::set_mod(1e8); int n, r; cin >> n >> r; if (n < r) quit(0); if (r > n-r) r = n-r; mint p = 1; int cnt2 = 0, cnt5 = 0; auto decomp = [&](int x) -> tuple { int cnt2 = 0, cnt5 = 0; while (x % 2 == 0) cnt2++, x /= 2; while (x % 5 == 0) cnt5++, x /= 5; return { x, cnt2, cnt5 }; }; rep (i, r) { { auto [x, c2, c5] = decomp(n-i); p *= x; cnt2 += c2; cnt5 += c5; } { auto [x, c2, c5] = decomp(i+1); p /= x; cnt2 -= c2; cnt5 -= c5; } } dump(p, cnt2, cnt5); assert(cnt2 >= 0 and cnt5 >= 0); p *= mint(2).pow(cnt2); p *= mint(5).pow(cnt5); cout << setfill('0') << setw(8) << p << '\n'; }