結果
問題 | No.2461 一点張り |
ユーザー | ttttan2 |
提出日時 | 2023-09-09 23:16:14 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 5 ms / 2,000 ms |
コード長 | 46,012 bytes |
コンパイル時間 | 2,827 ms |
コンパイル使用メモリ | 218,464 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-06-27 15:42:35 |
合計ジャッジ時間 | 3,534 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 3 ms
5,376 KB |
testcase_02 | AC | 4 ms
5,376 KB |
testcase_03 | AC | 4 ms
5,376 KB |
testcase_04 | AC | 3 ms
5,376 KB |
testcase_05 | AC | 4 ms
5,376 KB |
testcase_06 | AC | 5 ms
5,376 KB |
testcase_07 | AC | 2 ms
5,376 KB |
ソースコード
#include <algorithm>#include <bitset>#include <complex>#include <cstring>#include <deque>#include <exception>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iosfwd>#include <iostream>#include <istream>#include <iterator>#include <limits>#include <list>#include <locale>#include <map>#include <memory>#include <new>#include <numeric>#include <ostream>#include <queue>#include <set>#include <sstream>#include <stack>#include <stdexcept>#include <streambuf>#include <string>#include <typeinfo>#include <utility>#include <valarray>#include <vector>#if __cplusplus >= 201103L#include <array>#include <atomic>#include <chrono>#include <condition_variable>#include <forward_list>#include <future>#include <initializer_list>#include <mutex>#include <random>#include <ratio>#include <regex>#include <scoped_allocator>#include <system_error>#include <thread>#include <tuple>#include <typeindex>#include <type_traits>#include <unordered_map>#include <unordered_set>#endifusing namespace std;typedef long long ll;typedef unsigned long long ull;typedef unsigned int ui;typedef pair<int,int> pii;typedef pair<pii,int> ppii;typedef pair<int,pii> pipi;typedef pair<ll,ll> pll;typedef pair<pll,ll> ppll;typedef pair<ll,pll> plpl;typedef pair<pii,pii> pippi;typedef tuple<ll,ll,ll> tl;typedef pair<long double,long double> pdd;//typedef vector<vector<ll>> mat;const ll mod=1000000007;const ll mod2=998244353;const ll mod3=1000000009;ll inf=numeric_limits<ll>::max()/2;int iinf=numeric_limits<int>::max()/2;double pi=3.14159265358979323846;double eps=1e-8;#define rep(i,m,n) for(ll i=m;i<n;i++)#define rrep(i,n,m) for(ll i=n;i>=m;i--)#define srep(itr,st) for(auto itr=st.begin();itr!=st.end();itr++)#define mrep(itr,mp) for(auto& itr:mp)#define Max(a,b) a=max(a,b)#define Min(a,b) a=min(a,b)int dh[4]={1,0,-1,0};int dw[4]={0,1,0,-1};int ddh[8]={-1,-1,-1,0,0,1,1,1};int ddw[8]={-1,0,1,-1,1,-1,0,1};struct custom_hash {static uint64_t splitmix64(uint64_t x) {x+=0x9e3779b97f4a7c15;x=(x^(x>>30))*0xbf58476d1ce4e5b9;x=(x^(x>>27))*0x94d049bb133111eb;return x^(x>>31);}size_t operator()(uint64_t x) const {static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();return splitmix64(x + FIXED_RANDOM);}};#define umh unordered_map<int,ll,custom_hash>ll gcd(ll a,ll b){if(a<0)a=-a;if(b<0)b=-b;if(a<b)swap(a,b);if(b==0)return a;if(a%b==0)return b;return gcd(b,a%b);}ll lcm(ll a,ll b){if(a==0)return b;if(b==0)return a;ll c=gcd(a,b);a/=c;a*=b;return a;}ll Pow(ll n,ll k){if(k<0)return 0;ll ret=1;ll now=n;while(k>0){if(k&1)ret*=now;now*=now;k/=2;}return ret;}ll beki(ll n,ll k,ll md){ll ret=1;ll now=n;now%=md;while(k>0){if(k%2==1){ret*=now;ret%=md;}now*=now;now%=md;k=k>>1;}return ret;}ll gyaku(ll n,ll md){return beki(n,md-2,md);}ll popcount(ll n){ll ret=0;ll u=n;while(u>0){ret+=u%2;u/=2;}return ret;}#ifndef ATCODER_INTERNAL_BITOP_HPP#define ATCODER_INTERNAL_BITOP_HPP 1#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}}}#endif#ifndef ATCODER_INTERNAL_MATH_HPP#define ATCODER_INTERNAL_MATH_HPP 1#include <utility>namespace atcoder {namespace internal {constexpr long long safe_mod(long long x, long long m) {x%=m;if(x<0)x+=m;return x;}struct barrett {unsigned int _m;unsigned long long im;barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n<=1) return false;if (n==2||n==7||n==61) return true;if (n%2==0) return false;long long d = n - 1;while (d%2==0)d/=2;for (long long a : {2, 7, 61}) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root = primitive_root_constexpr(m);unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}}}#endif#ifndef ATCODER_INTERNAL_QUEUE_HPP#define ATCODER_INTERNAL_QUEUE_HPP 1#include <vector>namespace atcoder {namespace internal {template <class T> struct simple_queue {std::vector<T> payload;int pos = 0;void reserve(int n) { payload.reserve(n); }int size() const { return int(payload.size()) - pos; }bool empty() const { return pos == int(payload.size()); }void push(const T& t) { payload.push_back(t); }T& front() { return payload[pos]; }void clear() {payload.clear();pos = 0;}void pop() { pos++; }};}}#endif#ifndef ATCODER_INTERNAL_SCC_HPP#define ATCODER_INTERNAL_SCC_HPP 1#include <algorithm>#include <utility>#include <vector>namespace atcoder {namespace internal {template <class E> struct csr {std::vector<int> start;std::vector<E> elist;csr(int n, const std::vector<std::pair<int, E>>& edges): start(n + 1), elist(edges.size()) {for (auto e : edges) {start[e.first + 1]++;}for (int i = 1; i <= n; i++) {start[i] += start[i - 1];}auto counter = start;for (auto e : edges) {elist[counter[e.first]++] = e.second;}}};struct scc_graph {public:scc_graph(int n) : _n(n) {}int num_vertices() { return _n; }void add_edge(int from, int to) { edges.push_back({from, {to}}); }std::pair<int, std::vector<int>> scc_ids() {auto g = csr<edge>(_n, edges);int now_ord = 0, group_num = 0;std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);visited.reserve(_n);auto dfs = [&](auto self, int v) -> void {low[v] = ord[v] = now_ord++;visited.push_back(v);for (int i = g.start[v]; i < g.start[v + 1]; i++) {auto to = g.elist[i].to;if (ord[to] == -1) {self(self, to);low[v] = std::min(low[v], low[to]);} else {low[v] = std::min(low[v], ord[to]);}}if (low[v] == ord[v]) {while (true) {int u = visited.back();visited.pop_back();ord[u] = _n;ids[u] = group_num;if (u == v) break;}group_num++;}};for (int i = 0; i < _n; i++) {if (ord[i] == -1) dfs(dfs, i);}for (auto& x : ids) {x = group_num - 1 - x;}return {group_num, ids};}std::vector<std::vector<int>> scc() {auto ids = scc_ids();int group_num = ids.first;std::vector<int> counts(group_num);for (auto x : ids.second) counts[x]++;std::vector<std::vector<int>> groups(ids.first);for (int i = 0; i < group_num; i++) {groups[i].reserve(counts[i]);}for (int i = 0; i < _n; i++) {groups[ids.second[i]].push_back(i);}return groups;}private:int _n;struct edge {int to;};std::vector<std::pair<int, edge>> edges;};}}#endif#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1#include <cassert>#include <numeric>#include <type_traits>namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;}}#endif#ifndef ATCODER_MODINT_HPP#define ATCODER_MODINT_HPP 1#include <cassert>#include <numeric>#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;}template <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = internal::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;}}#endif#ifndef ATCODER_CONVOLUTION_HPP#define ATCODER_CONVOLUTION_HPP 1#include <algorithm>#include <array>#include <cassert>#include <type_traits>#include <vector>namespace atcoder {namespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30];if (first) {first = false;mint es[30], ies[30];int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30];if (first) {first = false;mint es[30], ies[30];int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) {if (n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}return ans;}int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721;static constexpr unsigned long long MOD2 = 167772161;static constexpr unsigned long long MOD3 = 469762049;static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}}#endif#ifndef ATCODER_DSU_HPP#define ATCODER_DSU_HPP 1#include <algorithm>#include <cassert>#include <vector>namespace atcoder {struct dsu {public:dsu() : _n(0) {}dsu(int n) : _n(n), parent_or_size(n, -1) {}int merge(int a, int b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);int x = leader(a), y = leader(b);if (x == y) return x;if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);parent_or_size[x] += parent_or_size[y];parent_or_size[y] = x;return x;}bool same(int a, int b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);return leader(a) == leader(b);}int leader(int a) {assert(0 <= a && a < _n);if (parent_or_size[a] < 0) return a;return parent_or_size[a] = leader(parent_or_size[a]);}int size(int a) {assert(0 <= a && a < _n);return -parent_or_size[leader(a)];}std::vector<std::vector<int>> groups() {std::vector<int> leader_buf(_n), group_size(_n);for (int i = 0; i < _n; i++) {leader_buf[i] = leader(i);group_size[leader_buf[i]]++;}std::vector<std::vector<int>> result(_n);for (int i = 0; i < _n; i++) {result[i].reserve(group_size[i]);}for (int i = 0; i < _n; i++) {result[leader_buf[i]].push_back(i);}result.erase(std::remove_if(result.begin(), result.end(),[&](const std::vector<int>& v) { return v.empty(); }),result.end());return result;}private:int _n;std::vector<int> parent_or_size;};}#endif#ifndef ATCODER_FENWICKTREE_HPP#define ATCODER_FENWICKTREE_HPP 1#include <cassert>#include <vector>namespace atcoder {template <class T> struct fenwick_tree {using U = internal::to_unsigned_t<T>;public:fenwick_tree() : _n(0) {}fenwick_tree(int n) : _n(n), data(n) {}void add(int p, T x) {assert(0 <= p && p < _n);p++;while (p <= _n) {data[p - 1] += U(x);p += p & -p;}}void change(int p,T x){add(p,x-data[p]);}T sum(int l, int r) {assert(0 <= l && l <= r && r <= _n);return sum(r) - sum(l);}int lb(T w){if(w<=0)return 0;int x=0;int u=1;while(u<_n)u*=2;for(int k=u;k>0;k/=2){if(x+k<=_n&&data[x+k-1]<w){w-=data[x+k-1];x+=k;}}return x;}private:int _n;std::vector<U> data;U sum(int r) {U s = 0;while (r > 0) {s += data[r - 1];r -= r & -r;}return s;}};}#endif#ifndef ATCODER_LAZYSEGTREE_HPP#define ATCODER_LAZYSEGTREE_HPP 1#include <algorithm>#include <cassert>#include <iostream>#include <vector>namespace atcoder {template <class S,S (*op)(S, S),S (*e)(),class F,S (*mapping)(F, S),F (*composition)(F, F),F (*id)()>struct lazy_segtree {public:lazy_segtree() : lazy_segtree(0) {}lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {log = internal::ceil_pow2(_n);size = 1 << log;d = std::vector<S>(2 * size, e());lz = std::vector<F>(size, id());for (int i = 0; i < _n; i++) d[size + i] = v[i];for (int i = size - 1; i >= 1; i--) {update(i);}}void set(int p, S x) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);d[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);return d[p];}S prod(int l, int r) {assert(0 <= l && l <= r && r <= _n);if (l == r) return e();l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push(r >> i);}S sml = e(), smr = e();while (l < r) {if (l & 1) sml = op(sml, d[l++]);if (r & 1) smr = op(d[--r], smr);l >>= 1;r >>= 1;}return op(sml, smr);}S all_prod() { return d[1]; }void apply(int p, F f) {assert(0 <= p && p < _n);p += size;for (int i = log; i >= 1; i--) push(p >> i);d[p] = mapping(f, d[p]);for (int i = 1; i <= log; i++) update(p >> i);}void apply(int l, int r, F f) {assert(0 <= l && l <= r && r <= _n);if (l == r) return;l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push((r - 1) >> i);}{int l2 = l, r2 = r;while (l < r) {if (l & 1) all_apply(l++, f);if (r & 1) all_apply(--r, f);l >>= 1;r >>= 1;}l = l2;r = r2;}for (int i = 1; i <= log; i++) {if (((l >> i) << i) != l) update(l >> i);if (((r >> i) << i) != r) update((r - 1) >> i);}}template <bool (*g)(S)> int max_right(int l) {return max_right(l, [](S x) { return g(x); });}template <class G> int max_right(int l, G g) {assert(0 <= l && l <= _n);assert(g(e()));if (l == _n) return _n;l += size;for (int i = log; i >= 1; i--) push(l >> i);S sm = e();do {while (l % 2 == 0) l >>= 1;if (!g(op(sm, d[l]))) {while (l < size) {push(l);l = (2 * l);if (g(op(sm, d[l]))) {sm = op(sm, d[l]);l++;}}return l - size;}sm = op(sm, d[l]);l++;} while ((l & -l) != l);return _n;}template <bool (*g)(S)> int min_left(int r) {return min_left(r, [](S x) { return g(x); });}template <class G> int min_left(int r, G g) {assert(0 <= r && r <= _n);assert(g(e()));if (r == 0) return 0;r += size;for (int i = log; i >= 1; i--) push((r - 1) >> i);S sm = e();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!g(op(d[r], sm))) {while (r < size) {push(r);r = (2 * r + 1);if (g(op(d[r], sm))) {sm = op(d[r], sm);r--;}}return r + 1 - size;}sm = op(d[r], sm);} while ((r & -r) != r);return 0;}private:int _n, size, log;std::vector<S> d;std::vector<F> lz;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }void all_apply(int k, F f) {d[k] = mapping(f, d[k]);if (k < size) lz[k] = composition(f, lz[k]);}void push(int k) {all_apply(2 * k, lz[k]);all_apply(2 * k + 1, lz[k]);lz[k] = id();}};}#endif#ifndef ATCODER_MAXFLOW_HPP#define ATCODER_MAXFLOW_HPP 1#include <algorithm>#include <cassert>#include <limits>#include <queue>#include <vector>namespace atcoder {template <class Cap> struct mf_graph {public:mf_graph() : _n(0) {}mf_graph(int n) : _n(n), g(n) {}int add_edge(int from, int to, Cap cap) {assert(0 <= from && from < _n);assert(0 <= to && to < _n);assert(0 <= cap);int m = int(pos.size());pos.push_back({from, int(g[from].size())});g[from].push_back(_edge{to, int(g[to].size()), cap});g[to].push_back(_edge{from, int(g[from].size()) - 1, 0});return m;}struct edge {int from, to;Cap cap, flow;};edge get_edge(int i) {int m = int(pos.size());assert(0 <= i && i < m);auto _e = g[pos[i].first][pos[i].second];auto _re = g[_e.to][_e.rev];return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};}std::vector<edge> edges() {int m = int(pos.size());std::vector<edge> result;for (int i = 0; i < m; i++) {result.push_back(get_edge(i));}return result;}void change_edge(int i, Cap new_cap, Cap new_flow) {int m = int(pos.size());assert(0 <= i && i < m);assert(0 <= new_flow && new_flow <= new_cap);auto& _e = g[pos[i].first][pos[i].second];auto& _re = g[_e.to][_e.rev];_e.cap = new_cap - new_flow;_re.cap = new_flow;}Cap flow(int s, int t) {return flow(s, t, std::numeric_limits<Cap>::max());}Cap flow(int s, int t, Cap flow_limit) {assert(0 <= s && s < _n);assert(0 <= t && t < _n);std::vector<int> level(_n), iter(_n);internal::simple_queue<int> que;auto bfs = [&]() {std::fill(level.begin(), level.end(), -1);level[s] = 0;que.clear();que.push(s);while (!que.empty()) {int v = que.front();que.pop();for (auto e : g[v]) {if (e.cap == 0 || level[e.to] >= 0) continue;level[e.to] = level[v] + 1;if (e.to == t) return;que.push(e.to);}}};auto dfs = [&](auto self, int v, Cap up) {if (v == s) return up;Cap res = 0;int level_v = level[v];for (int& i = iter[v]; i < int(g[v].size()); i++) {_edge& e = g[v][i];if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;Cap d =self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));if (d <= 0) continue;g[v][i].cap += d;g[e.to][e.rev].cap -= d;res += d;if (res == up) break;}return res;};Cap flow = 0;while (flow < flow_limit) {bfs();if (level[t] == -1) break;std::fill(iter.begin(), iter.end(), 0);while (flow < flow_limit) {Cap f = dfs(dfs, t, flow_limit - flow);if (!f) break;flow += f;}}return flow;}std::vector<bool> min_cut(int s) {std::vector<bool> visited(_n);internal::simple_queue<int> que;que.push(s);while (!que.empty()) {int p = que.front();que.pop();visited[p] = true;for (auto e : g[p]) {if (e.cap && !visited[e.to]) {visited[e.to] = true;que.push(e.to);}}}return visited;}private:int _n;struct _edge {int to, rev;Cap cap;};std::vector<std::pair<int, int>> pos;std::vector<std::vector<_edge>> g;};}#endif#ifndef ATCODER_MINCOSTFLOW_HPP#define ATCODER_MINCOSTFLOW_HPP 1#include <algorithm>#include <cassert>#include <limits>#include <queue>#include <vector>namespace atcoder {template <class Cap, class Cost> struct mcf_graph {public:mcf_graph() {}mcf_graph(int n) : _n(n), g(n) {}int add_edge(int from, int to, Cap cap, Cost cost) {assert(0 <= from && from < _n);assert(0 <= to && to < _n);int m = int(pos.size());pos.push_back({from, int(g[from].size())});g[from].push_back(_edge{to, int(g[to].size()), cap, cost});g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost});return m;}struct edge {int from, to;Cap cap, flow;Cost cost;};edge get_edge(int i) {int m = int(pos.size());assert(0 <= i && i < m);auto _e = g[pos[i].first][pos[i].second];auto _re = g[_e.to][_e.rev];return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,};}std::vector<edge> edges() {int m = int(pos.size());std::vector<edge> result(m);for (int i = 0; i < m; i++) {result[i] = get_edge(i);}return result;}std::pair<Cap, Cost> flow(int s, int t) {return flow(s, t, std::numeric_limits<Cap>::max());}std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {return slope(s, t, flow_limit).back();}std::vector<std::pair<Cap, Cost>> slope(int s, int t) {return slope(s, t, std::numeric_limits<Cap>::max());}std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {assert(0 <= s && s < _n);assert(0 <= t && t < _n);assert(s != t);std::vector<Cost> dual(_n, 0), dist(_n);std::vector<int> pv(_n), pe(_n);std::vector<bool> vis(_n);auto dual_ref = [&]() {std::fill(dist.begin(), dist.end(),std::numeric_limits<Cost>::max());std::fill(pv.begin(), pv.end(), -1);std::fill(pe.begin(), pe.end(), -1);std::fill(vis.begin(), vis.end(), false);struct Q {Cost key;int to;bool operator<(Q r) const { return key > r.key; }};std::priority_queue<Q> que;dist[s] = 0;que.push(Q{0, s});while (!que.empty()) {int v = que.top().to;que.pop();if (vis[v]) continue;vis[v] = true;if (v == t) break;for (int i = 0; i < int(g[v].size()); i++) {auto e = g[v][i];if (vis[e.to] || !e.cap) continue;Cost cost = e.cost - dual[e.to] + dual[v];if (dist[e.to] - dist[v] > cost) {dist[e.to] = dist[v] + cost;pv[e.to] = v;pe[e.to] = i;que.push(Q{dist[e.to], e.to});}}}if (!vis[t]) {return false;}for (int v = 0; v < _n; v++) {if (!vis[v]) continue;dual[v] -= dist[t] - dist[v];}return true;};Cap flow = 0;Cost cost = 0, prev_cost = -1;std::vector<std::pair<Cap, Cost>> result;result.push_back({flow, cost});while (flow < flow_limit) {if (!dual_ref()) break;Cap c = flow_limit - flow;for (int v = t; v != s; v = pv[v]) {c = std::min(c, g[pv[v]][pe[v]].cap);}for (int v = t; v != s; v = pv[v]) {auto& e = g[pv[v]][pe[v]];e.cap -= c;g[v][e.rev].cap += c;}Cost d = -dual[s];flow += c;cost += c * d;if (prev_cost == d) {result.pop_back();}result.push_back({flow, cost});prev_cost = cost;}return result;}private:int _n;struct _edge {int to, rev;Cap cap;Cost cost;};std::vector<std::pair<int, int>> pos;std::vector<std::vector<_edge>> g;};}#endif#ifndef ATCODER_SEGTREE_HPP#define ATCODER_SEGTREE_HPP 1#include <algorithm>#include <cassert>#include <vector>namespace atcoder {template <class S, S (*op)(S, S), S (*e)()> struct segtree {public:segtree() : segtree(0) {}segtree(int n) : segtree(std::vector<S>(n, e())) {}segtree(const std::vector<S>& v) : _n(int(v.size())) {log = internal::ceil_pow2(_n);size = 1 << log;d = std::vector<S>(2 * size, e());for (int i = 0; i < _n; i++) d[size + i] = v[i];for (int i = size - 1; i >= 1; i--) {update(i);}}void set(int p, S x) {assert(0 <= p && p < _n);p += size;d[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);return d[p + size];}S prod(int l, int r) {assert(0 <= l && l <= r && r <= _n);S sml = e(), smr = e();l += size;r += size;while (l < r) {if (l & 1) sml = op(sml, d[l++]);if (r & 1) smr = op(d[--r], smr);l >>= 1;r >>= 1;}return op(sml, smr);}S all_prod() { return d[1]; }template <bool (*f)(S)> int max_right(int l) {return max_right(l, [](S x) { return f(x); });}template <class F> int max_right(int l, F f) {assert(0 <= l && l <= _n);assert(f(e()));if (l == _n) return _n;l += size;S sm = e();do {while (l % 2 == 0) l >>= 1;if (!f(op(sm, d[l]))) {while (l < size) {l = (2 * l);if (f(op(sm, d[l]))) {sm = op(sm, d[l]);l++;}}return l - size;}sm = op(sm, d[l]);l++;} while ((l & -l) != l);return _n;}template <bool (*f)(S)> int min_left(int r) {return min_left(r, [](S x) { return f(x); });}template <class F> int min_left(int r, F f) {assert(0 <= r && r <= _n);assert(f(e()));if (r == 0) return 0;r += size;S sm = e();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!f(op(d[r], sm))) {while (r < size) {r = (2 * r + 1);if (f(op(d[r], sm))) {sm = op(d[r], sm);r--;}}return r + 1 - size;}sm = op(d[r], sm);} while ((r & -r) != r);return 0;}private:int _n, size, log;std::vector<S> d;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }};}#endifusing namespace atcoder;#define endl "\n"using mint=static_modint<mod2>;int main(){ios::sync_with_stdio(false);cin.tie(nullptr);int t;cin>>t;rep(_,0,t){double p;int k;cin>>p>>k;double ans=0;double np=1;rep(i,1,k){ans+=np*p*i;np*=1-p;}ans+=np*k;cout<<fixed<<setprecision(12)<<ans<<endl;}}