#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; using dmint = modint; int p; constexpr int FACT_SIZE = 1000000; dmint Fact[FACT_SIZE + 1]; dmint iFact[FACT_SIZE + 1]; const auto fact_init = [] { int FACT_SIZE = p - 1; Fact[0] = dmint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }; dmint comb(int n, int k) { if (k == 0) return dmint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return dmint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } dmint icomb(int n, int k) { return iFact[n] * Fact[n - k] * Fact[k]; } dmint fact(int n) {return Fact[n];} dmint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } } int main() { ios::sync_with_stdio(false); cin.tie(0); ll n; cin >> n >> p; dmint::set_mod(p); fact_init(); int r = internal::primitive_root_constexpr(p); VI val2e(p), e2val(p); { int v = 1; for (int e = 0; e < p - 1; e++) { val2e[v] = e; e2val[e] = v; v = ll(v * r) % p; } assert(v == 1); } vector f(p - 1); f[0] = 1; while (n) { int m = n % p; n /= p; vector g(p - 1); rep(i, m + 1) g[val2e[comb(m, i).val()]]++; f = convolution(f, g); while (ssize(f) > p - 1) { f[ssize(f) - 1 - (p - 1)] += f[ssize(f) - 1]; f.pop_back(); } } mint ans; rep(e, p - 1) ans += e2val[e] * f[e]; cout << ans.val() << '\n'; }