#include using namespace std; typedef long long ll; typedef pair pll; typedef pair pii; typedef pair pdd; typedef vector vi; typedef vector vll; typedef vector vd; typedef vector vs; typedef vector vvi; typedef vector vvvi; typedef vector vvll; typedef vector vvvll; typedef vector vpii; typedef vector vvpii; typedef vector vpll; typedef vector vvpll; typedef vector vpdd; typedef vector vvd; #define yn(ans) printf("%s\n", (ans)?"Yes":"No"); #define YN(ans) printf("%s\n", (ans)?"YES":"NO"); template bool chmax(T &a, T b) { if (a >= b) return false; a = b; return true; } template bool chmin(T &a, T b) { if (a <= b) return false; a = b; return true; } #define FOR(i, s, e, t) for ((i) = (s); (i) < (e); (i) += (t)) #define REP(i, e) for (int i = 0; i < (e); ++i) #define REP1(i, s, e) for (int i = (s); i < (e); ++i) #define RREP(i, e) for (int i = (e); i >= 0; --i) #define RREP1(i, e, s) for (int i = (e); i >= (s); --i) #define all(v) v.begin(), v.end() #define pb push_back #define qb pop_back #define pf push_front #define qf pop_front #define maxe max_element #define mine min_element ll inf = 1e18; #define DEBUG printf("%d\n", __LINE__); fflush(stdout); template void print(vector &v, bool withSize = false) { if (withSize) cout << v.size() << endl; REP(i, v.size()) cout << v[i] << " "; cout << endl; } mt19937_64 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count()); int __FAST_IO__ = []() { std::ios::sync_with_stdio(0); std::cin.tie(0); std::cout.tie(0); return 0; }(); // Mint & Combinatorics template T inverse(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } return u; } template class Modular { public: using Type = typename decay::type; constexpr Modular() : value() {} template Modular(const U& x) { value = normalize(x); } template static Type normalize(const U& x) { Type v; if (-mod() <= x && x < mod()) v = static_cast(x); else v = static_cast(x % mod()); if (v < 0) v += mod(); return v; } const Type& operator()() const { return value; } template explicit operator U() const { return static_cast(value); } constexpr static Type mod() { return T::value; } Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; } template Modular& operator+=(const U& other) { return *this += Modular(other); } template Modular& operator-=(const U& other) { return *this -= Modular(other); } Modular& operator++() { return *this += 1; } Modular& operator--() { return *this -= 1; } Modular operator++(int) { Modular result(*this); *this += 1; return result; } Modular operator--(int) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); } template typename enable_if::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) { #ifdef _WIN32 uint64_t x = static_cast(value) * static_cast(rhs.value); uint32_t xh = static_cast(x >> 32), xl = static_cast(x), d, m; asm( "divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (mod()) ); value = m; #else value = normalize(static_cast(value) * static_cast(rhs.value)); #endif return *this; } template typename enable_if::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) { long long q = static_cast(static_cast(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template typename enable_if::Type>::value, Modular>::type& operator*=(const Modular& rhs) { value = normalize(value * rhs.value); return *this; } Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); } friend const Type& abs(const Modular& x) { return x.value; } template friend bool operator==(const Modular& lhs, const Modular& rhs); template friend bool operator<(const Modular& lhs, const Modular& rhs); template friend V& operator>>(V& stream, Modular& number); private: Type value; }; template bool operator==(const Modular& lhs, const Modular& rhs) { return lhs.value == rhs.value; } template bool operator==(const Modular& lhs, U rhs) { return lhs == Modular(rhs); } template bool operator==(U lhs, const Modular& rhs) { return Modular(lhs) == rhs; } template bool operator!=(const Modular& lhs, const Modular& rhs) { return !(lhs == rhs); } template bool operator!=(const Modular& lhs, U rhs) { return !(lhs == rhs); } template bool operator!=(U lhs, const Modular& rhs) { return !(lhs == rhs); } template bool operator<(const Modular& lhs, const Modular& rhs) { return lhs.value < rhs.value; } template Modular operator+(const Modular& lhs, const Modular& rhs) { return Modular(lhs) += rhs; } template Modular operator+(const Modular& lhs, U rhs) { return Modular(lhs) += rhs; } template Modular operator+(U lhs, const Modular& rhs) { return Modular(lhs) += rhs; } template Modular operator-(const Modular& lhs, const Modular& rhs) { return Modular(lhs) -= rhs; } template Modular operator-(const Modular& lhs, U rhs) { return Modular(lhs) -= rhs; } template Modular operator-(U lhs, const Modular& rhs) { return Modular(lhs) -= rhs; } template Modular operator*(const Modular& lhs, const Modular& rhs) { return Modular(lhs) *= rhs; } template Modular operator*(const Modular& lhs, U rhs) { return Modular(lhs) *= rhs; } template Modular operator*(U lhs, const Modular& rhs) { return Modular(lhs) *= rhs; } template Modular operator/(const Modular& lhs, const Modular& rhs) { return Modular(lhs) /= rhs; } template Modular operator/(const Modular& lhs, U rhs) { return Modular(lhs) /= rhs; } template Modular operator/(U lhs, const Modular& rhs) { return Modular(lhs) /= rhs; } template Modular power(const Modular& a, const U& b) { assert(b >= 0); Modular x = a, res = 1; U p = b; while (p > 0) { if (p & 1) res *= x; x *= x; p >>= 1; } return res; } template bool IsZero(const Modular& number) { return number() == 0; } template string to_string(const Modular& number) { return to_string(number()); } // U == std::ostream? but done this way because of fastoutput template U& operator<<(U& stream, const Modular& number) { return stream << number(); } // U == std::istream? but done this way because of fastinput template U& operator>>(U& stream, Modular& number) { typename common_type::Type, long long>::type x; stream >> x; number.value = Modular::normalize(x); return stream; } struct MOD { static int value; }; int MOD::value = 998244353; using Mint = Modular; typedef vector vm; typedef vector vvm; typedef vector vvvm; vector fac, ifac; void initFac(int N) { fac.resize(N + 1); ifac.resize(N + 1); fac[0] = ifac[0] = 1; REP1(i, 1, N + 1) { fac[i] = fac[i - 1] * i; } ifac[N] = 1 / fac[N]; RREP1(i, N - 1, 1) { ifac[i] = (i + 1) * ifac[i + 1]; } } Mint C(int m, int n) { if (m < n || n < 0) return 0; return fac[m] * ifac[n] * ifac[m - n]; } Mint P(int m, int n) { if (m < n || n < 0) return 0; return fac[m] * ifac[m - n]; } template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { vector< Mint > dw, idw; int max_base; Mint root; NumberTheoreticTransformFriendlyModInt() { const unsigned mod = Mint::mod(); assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(power(root, (mod - 1) >> 1) == 1) root += 1; assert(power(root, mod - 1) == 1); dw.resize(max_base); idw.resize(max_base); for(int i = 0; i < max_base; i++) { dw[i] = -power(root, (mod - 1) >> (i + 2)); idw[i] = Mint(1) / dw[i]; } } void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = n; m >>= 1;) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; a[i] = x + y, a[j] = x - y; } w *= dw[__builtin_ctz(++k)]; } } } void intt(vector< Mint > &a, bool f = true) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = 1; m < n; m *= 2) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * w; } w *= idw[__builtin_ctz(++k)]; } } if(f) { Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } } vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); return a; } void sq(vector &a, vector &b, bool mult) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; b.resize(sz, 0); ntt(b); Mint inv_sz = Mint(1) / sz; if (mult) { a.resize(sz, 0); ntt(a); for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); } for (int i = 0; i < sz; i++) b[i] *= b[i] * inv_sz; intt(b, false); b.resize(need); } void pow(vector &a, vector &b, int p) { int len = a.size(); while (p) { sq(a, b, p & 1); a.resize(len); b.resize(len); p >>= 1; } } }; NumberTheoreticTransformFriendlyModInt ntt; #define TESTS int t; cin >> t; while (t--) #define TEST int main() { int N, X; cin >> N >> X; initFac(N); Mint p = Mint(X) / 100; vm pw(N + 1, 1), qw(N + 1, 1); REP(i, N) pw[i + 1] = pw[i] * p, qw[i + 1] = qw[i] * (1 - p); vvm dp(N + 1, vm(N + 1, 0)); dp[1][N - 1] = 1; RREP1(tot, N, 1) { // REP(j, tot + 1) printf("%d %d %d\n", tot - j, j, dp[tot - j][j]); vm A(tot + 1, 0), B(tot + 1, 0); REP(j, tot + 1) { if (j < tot) A[j] = dp[tot - j][j] * fac[j]; B[tot - j] = pw[j] * ifac[j]; } // print(A), print(B); vm C = ntt.multiply(A, B); // print(C); REP1(j, tot, C.size()) { int nj = j - tot, ni = tot - 1 - nj; if (ni >= 0) dp[ni][nj] = C[j] * qw[nj] * ifac[nj]; } } Mint ans = 0; REP(i, N + 1) { ans += dp[0][i] * (N - i); } printf("%d\n", ans); return 0; }