#include "bits/stdc++.h" #include #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define SZ(x) ((lint)(x).size()) #define FOR(i, begin, end) for(lint 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) #define endk '\n' using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef long double ld; typedef pair plint; typedef pair pld; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(10); }; } fast_ios_; template auto add = [](T a, T b) -> T { return a + b; }; template auto mul = [](T a, T b) -> T { return a * b; }; template auto f_max = [](T a, T b) -> T { return max(a, b); }; template auto f_min = [](T a, T b) -> T { return min(a, b); }; template using V = vector; using Vl = V; using VVl = V; using VVVl = V>; template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) { for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : ""); return os; } template< typename T >istream& operator>>(istream& is, vector< T >& v) { for (T& in : v) is >> in; return is; } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct rec { F f; rec(F&& f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; //lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); } lint digit(lint a) { return (lint)log10(a); } lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); } lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); } bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a >= limit / b; } // a * b > c => true void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); } const lint MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 1e18; lint dx[8] = { 0, 1, 0, -1, 1, -1, 1, -1 }, dy[8] = { 1, 0, -1, 0, -1, -1, 1, 1 }; bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; } struct Edge { lint from, to; lint cost; Edge() { } Edge(lint u, lint v, lint c) { cost = c; from = u; to = v; } bool operator<(const Edge& e) const { return cost < e.cost; } }; struct WeightedEdge { lint to; lint cost; WeightedEdge(lint v, lint c) { to = v; cost = c; } bool operator<(const WeightedEdge& e) const { return cost < e.cost; } }; using WeightedGraph = V>; typedef pair tlint; typedef pair pld; typedef pair qlint; typedef pair vstr; typedef pair valv; class smart_sieve { intmax_t L, R, M; std::vector small; // 小さい篩 std::vector> large; // 大きい篩 std::vector aux; // aux[i] := large[i] の素因数の積 public: smart_sieve(intmax_t L, intmax_t R) : L(L), R(R), M(sqrt(R) + 1) { small.resize(M); std::iota(small.begin(), small.end(), 0); large.resize(R - L); aux.assign(R - L, 1); for (intmax_t i = 2; i * i < R; ++i) { if (small[i] < i) continue; small[i] = i; for (intmax_t j = i * i; j < M; j += i) if (small[j] == j) small[j] = i; for (intmax_t j = (L + i - 1) / i * i; j < R; j += i) { intmax_t k = j; do { // aux[j-L] > M で判定した方がいいかも? // j / aux[j-L] < M の方がいい?(割り算したくない) if (aux[j - L] * aux[j - L] > R) break; large[j - L].push_back(i); aux[j - L] *= i; k /= i; } while (k % i == 0); } } } std::vector factor(intmax_t n) { assert(L <= n && n < R); std::vector res = large[n - L]; n /= aux[n - L]; if (n >= M) { // この場合,n は素数となることが示せる(はず) // n*n >= R だとオーバーフローしそう? res.push_back(n); return res; } while (n > 1) { res.push_back(small[n]); n /= small[n]; } return res; } }; int main() { lint N, M; cin >> N >> M; if (M > 100000) { cout << 0 << endk; return 0; } map cnt; smart_sieve sie1(N - M - 100, N + 100), sie2(0, M + 100); REP(i, M) { { auto fac = sie1.factor(N - i); for (auto v : fac) cnt[v]++; } { auto fac = sie2.factor(i + 1); for (auto v : fac) cnt[v]--; } } lint ans = 1; for (auto p : cnt) { REP(i, p.second) { ans *= p.first; ans %= 100000000; } } string _ans = to_string(ans); reverse(ALL(_ans)); while (SZ(_ans) < 8) _ans += '0'; reverse(ALL(_ans)); cout << _ans << endk; }