結果
問題 | No.2569 はじめてのおつかいHard |
ユーザー |
![]() |
提出日時 | 2023-12-05 12:22:32 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 257 ms / 2,000 ms |
コード長 | 36,284 bytes |
コンパイル時間 | 4,653 ms |
コンパイル使用メモリ | 246,900 KB |
実行使用メモリ | 37,732 KB |
最終ジャッジ日時 | 2024-09-27 00:13:01 |
合計ジャッジ時間 | 6,976 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 10 |
ソースコード
#include "bits/stdc++.h"#include <numeric>#include <atcoder/all>using namespace std;using namespace atcoder;// clang-format off/* accelration */// 高速バイナリ生成#pragma GCC target("avx")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")// cin cout の結びつけ解除, stdioと同期しない(入出力非同期化)// cとstdの入出力を混在させるとバグるので注意struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;using mint9 = modint998244353;/* alias */using ull = unsigned long long;using ll = long long;using vi = vector<int>;using vl = vector<long>;using vll = vector<long long>;using vvi = vector<vi>;using vvl = vector<vl>;using vvll = vector<vll>;using vvvll = vector<vvll>;using vd = vector<double>;using vs = vector<string>;using pii = pair<int, int>;using pll = pair<ll, ll>;using pdd = pair<double, double>;using vb = vector<bool>;using vvb = vector<vb>;using vpii = vector<pii>;using vpll = vector<pll>;using vpdd = vector<pdd>;using vm = vector<mint9>;using vvm = vector<vm>;using vvvm = vector<vvm>;using vs = vector<string>;/* define short */#define pb push_back// #define mp make_pair#define all(obj) (obj).begin(), (obj).end()#define YESNO(bool) if(bool){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}#define yesno(bool) if(bool){cout<<"yes"<<endl;}else{cout<<"no"<<endl;}#define YesNo(bool) if(bool){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}/* REP macro */#define reps(i, a, n) for (ll i = (a); i < (ll)(n); ++i)#define rep(i, n) reps(i, 0, n)#define rrep(i, n) reps(i, 1, n + 1)#define repd(i,n) for(ll i=n-1;i>=0;i--)#define rrepd(i,n) for(ll i=n;i>=1;i--)#define repsd(i, a, n) for(ll i=n;i>=a;i--)#define fore(i,a) for(auto &i:a)/* 追加分 */#define vsort(v) sort(v.begin(), v.end())#define verase(v) v.erase(unique(v.begin(), v.end()), v.end())#define vlb(v, x) lower_bound(v.begin(), v.end(), x) - v.begin()#define argsort(v) sort(xy.begin(), xy.end(), [](const auto &p1, const auto &p2) { return atan2l(p1.second, p1.first) < atan2l(p2.second, p2.first);})/* debug */// 標準エラー出力を含む提出はrejectされる場合もあるので注意#define debug(x) cerr << "\033[33m(line:" << __LINE__ << ") " << #x << ": " << x << "\033[m" << endl;/* int128 */#define __int128_t ll/* func */inline int in_int() { int x; cin >> x; return x; }inline ll in_ll() { ll x; cin >> x; return x; }inline string in_str() { string x; cin >> x; return x; }// search_length: 走査するベクトル長の上限(先頭から何要素目までを検索対象とするか、1始まりで)template <typename T> inline bool vector_finder(std::vector<T> vec, T element, unsigned int search_length) {auto itr = std::find(vec.begin(), vec.end(), element);size_t index = std::distance(vec.begin(), itr);if (index == vec.size() || index >= search_length) { return false; }else { return true; }}template <typename T> inline void print(const vector<T>& v, string s = " "){rep(i, v.size()) cout << v[i] << (i != (ll)v.size() - 1 ? s : "\n");}template <typename T, typename S> inline void print(const pair<T, S>& p){cout << p.first << " " << p.second << endl;}template <typename T> inline void print(const T& x) { cout << x << "\n"; }inline void printd(double x) { cout << fixed << setprecision(15) << x << endl; }template <typename T, typename S> inline void print(const vector<pair<T, S>>& v){for (auto&& p : v) print(p);}// 第一引数と第二引数を比較し、第一引数(a)をより大きい/小さい値に上書きtemplate <typename T> inline bool chmin(T& a, const T& b) { bool compare = a > b; if (a > b) a = b; return compare; }template <typename T> inline bool chmax(T& a, const T& b) { bool compare = a < b; if (a < b) a = b; return compare; }// gcd lcm// C++17からは標準実装// template <typename T> T gcd(T a, T b) {if (b == 0)return a; else return gcd(b, a % b);}// template <typename T> inline T lcm(T a, T b) {return (a * b) / gcd(a, b);}// clang-format on// 提出の際はコメントアウトすること// #define __builtin_ctzll _tzcnt_u64int alt__builtin_clz(unsigned int x){int rank = 0;while (x) {rank++;x >>= 1;}return 32 - rank;}static inline int alt__builtin_ctz(unsigned int x){rep(i, 32) {if (x & 1) return i;x >>= 1;}}static inline int alt__builtin_ctzll(unsigned long long x){rep(i, 64) {if (x & 1) return i;x >>= 1;}}template< typename T = int >struct Edge {int from, to;T cost;int idx;Edge() = default;Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {}operator int() const { return to; }};template< typename T = int >struct Graph {vector< vector< Edge< T > > > g;int es;Graph() = default;explicit Graph(int n) : g(n), es(0) {}size_t size() const {return g.size();}void add_directed_edge(int from, int to, T cost = 1) {g[from].emplace_back(from, to, cost, es++);}void add_edge(int from, int to, T cost = 1) {g[from].emplace_back(from, to, cost, es);g[to].emplace_back(to, from, cost, es++);}void read(int M, int padding = -1, bool weighted = false, bool directed = false) {for (int i = 0; i < M; i++) {int a, b;cin >> a >> b;a += padding;b += padding;T c = T(1);if (weighted) cin >> c;if (directed) add_directed_edge(a, b, c);else add_edge(a, b, c);}}inline vector< Edge< T > >& operator[](const int& k) {return g[k];}inline const vector< Edge< T > >& operator[](const int& k) const {return g[k];}};template< typename T = int >using Edges = vector< Edge< T > >;template< class T >struct Matrix {vector< vector< T > > A;Matrix() {}Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}Matrix(size_t n) : A(n, vector< T >(n, 0)) {};size_t height() const {return (A.size());}size_t width() const {return (A[0].size());}inline const vector< T >& operator[](int k) const {return (A.at(k));}inline vector< T >& operator[](int k) {return (A.at(k));}static Matrix I(size_t n) {Matrix mat(n);for (int i = 0; i < n; i++) mat[i][i] = 1;return (mat);}Matrix& operator+=(const Matrix& B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for (int i = 0; i < n; i++)for (int j = 0; j < m; j++)(*this)[i][j] += B[i][j];return (*this);}Matrix& operator-=(const Matrix& B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for (int i = 0; i < n; i++)for (int j = 0; j < m; j++)(*this)[i][j] -= B[i][j];return (*this);}Matrix& operator*=(const Matrix& B) {size_t n = height(), m = B.width(), p = width();assert(p == B.height());vector< vector< T > > C(n, vector< T >(m, 0));for (int i = 0; i < n; i++)for (int j = 0; j < m; j++)for (int k = 0; k < p; k++)C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);A.swap(C);return (*this);}Matrix& operator^=(long long k) {Matrix B = Matrix::I(height());while (k > 0) {if (k & 1) B *= *this;*this *= *this;k >>= 1LL;}A.swap(B.A);return (*this);}Matrix operator+(const Matrix& B) const {return (Matrix(*this) += B);}Matrix operator-(const Matrix& B) const {return (Matrix(*this) -= B);}Matrix operator*(const Matrix& B) const {return (Matrix(*this) *= B);}Matrix operator^(const long long k) const {return (Matrix(*this) ^= k);}friend ostream& operator<<(ostream& os, Matrix& p) {size_t n = p.height(), m = p.width();for (int i = 0; i < n; i++) {os << "[";for (int j = 0; j < m; j++) {os << p[i][j] << (j + 1 == m ? "]\n" : ",");}}return (os);}T determinant() {Matrix B(*this);assert(width() == height());T ret = 1;for (int i = 0; i < width(); i++) {int idx = -1;for (int j = i; j < width(); j++) {if (B[j][i] != 0) idx = j;}if (idx == -1) return (0);if (i != idx) {ret *= -1;swap(B[i], B[idx]);}ret *= B[i][i];T vv = B[i][i];for (int j = 0; j < width(); j++) {B[i][j] /= vv;}for (int j = i + 1; j < width(); j++) {T a = B[j][i];for (int k = 0; k < width(); k++) {B[j][k] -= B[i][k] * a;}}}return (ret);}};template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = (u64(0) - u64(mod)) % mod;static_assert(r* mod == 1, "invalid, r * mod != 1");static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t& b): a(reduce(u64(b% mod + mod)* n2)) {};static constexpr u32 reduce(const u64& b) {return (b + u64(u32(b) * u32(u32(0) - r)) * mod) >> 32;}constexpr mint& operator+=(const mint& b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint& operator-=(const mint& b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint& operator*=(const mint& b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint& operator/=(const mint& b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint& b) const { return mint(*this) += b; }constexpr mint operator-(const mint& b) const { return mint(*this) -= b; }constexpr mint operator*(const mint& b) const { return mint(*this) *= b; }constexpr mint operator/(const mint& b) const { return mint(*this) /= b; }constexpr bool operator==(const mint& b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint& b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const { return pow(mod - 2); }friend ostream& operator<<(ostream& os, const mint& b) {return os << b.get();}friend istream& operator>>(istream& is, mint& b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};template <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = 23;mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint>& a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[alt__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint>& a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[alt__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint>& a) {if ((int)a.size() <= 1) return;fft4(a, alt__builtin_ctz(a.size()));}void intt(vector<mint>& a) {if ((int)a.size() <= 1) return;ifft4(a, alt__builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for (auto& x : a) x *= iv;}vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;setwy(k);vector<mint> s(M), t(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(s, k);fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];ifft4(s, k);s.resize(l);mint invm = mint(M).inverse();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint>& a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS& operator+=(const FPS& r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS& operator+=(const mint& r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS& operator-=(const FPS& r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS& operator-=(const mint& r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS& operator*=(const mint& v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS& operator/=(const FPS& r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inverse();for (auto& x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS& operator%=(const FPS& r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS& r) const { return FPS(*this) += r; }FPS operator+(const mint& v) const { return FPS(*this) += v; }FPS operator-(const FPS& r) const { return FPS(*this) -= r; }FPS operator-(const mint& v) const { return FPS(*this) -= v; }FPS operator*(const FPS& r) const { return FPS(*this) *= r; }FPS operator*(const mint& v) const { return FPS(*this) *= v; }FPS operator/(const FPS& r) const { return FPS(*this) /= r; }FPS operator%(const FPS& r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}FPS pre(int sz) const {return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::get_mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto& v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert((*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void* ntt_ptr;static void set_fft();FPS& operator*=(const FPS& r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void* FormalPowerSeries<mint>::ntt_ptr = nullptr;template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint>*>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> res(deg);res[0] = { mint(1) / (*this)[0] };for (int d = 1; d < deg; d <<= 1) {FormalPowerSeries<mint> f(2 * d), g(2 * d);for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];for (int j = 0; j < d; j++) g[j] = res[j];f.ntt();g.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = 0; j < d; j++) f[j] = 0;f.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];}return res.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {using fps = FormalPowerSeries<mint>;assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = this->size();fps inv;inv.reserve(deg + 1);inv.push_back(mint(0));inv.push_back(mint(1));auto inplace_integral = [&](fps& F) -> void {const int n = (int)F.size();auto mod = mint::get_mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), mint(0));for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](fps& F) -> void {if (F.empty()) return;F.erase(begin(F));mint coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};fps b{ 1, 1 < (int)this->size() ? (*this)[1] : 0 }, c{ 1 }, z1, z2{ 1, 1 };for (int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);y.ntt();z1 = z2;fps z(m);for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];z.intt();fill(begin(z), begin(z) + m / 2, mint(0));z.ntt();for (int i = 0; i < m; ++i) z[i] *= -z1[i];z.intt();c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);z2.ntt();fps x(begin(*this), begin(*this) + min<int>(this->size(), m));x.resize(m);inplace_diff(x);x.push_back(mint(0));x.ntt();for (int i = 0; i < m; ++i) x[i] *= y[i];x.intt();x -= b.diff();x.resize(2 * m);for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];x.intt();x.pop_back();inplace_integral(x);for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];fill(begin(x), begin(x) + m, mint(0));x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];x.intt();b.insert(end(b), begin(x) + m, end(x));}return fps{ begin(b), begin(b) + deg };}template <typename T> inline void print(const FormalPowerSeries<T>& v, string s = " "){rep(i, v.size()) cout << v[i] << (i != (ll)v.size() - 1 ? s : "\n");}using mint = LazyMontgomeryModInt<998244353>;using fps = FormalPowerSeries<mint>;// 定数const ll INF = 1ll << 60;const vi dd({ -1,0,1,0,-1 });const double PI = atan(1) * 4;double eps = 1e-10;const ll MOD = 998244353;// 最大公約数ll gcd(ll a, ll b) {if (!b) return a;if (a % b == 0) return b;else return gcd(b, a % b);}// 最小公倍数ll lcm(ll a, ll b) {return a * b / gcd(a, b);}// インタラクティブ用void question(vll v) {cout << "?";rep(i, v.size()) {cout << " " << v[i];}cout << endl;}void answer(vll v) {cout << "!";rep(i, v.size()) {cout << " " << v[i];}cout << endl;}// 等差数列ll arith_sum1(ll left, ll right, ll d) {return (left + right) * (right - left + d) / (2 * d);}ll arith_sum2(ll left, ll d, ll num) {return arith_sum1(left, left + d * (num - 1), d);}// 座標圧縮void comp(vll& a) {sort(a.begin(), a.end());a.erase(unique(a.begin(), a.end()), a.end());}// 区間min(+idx)遅延セグ木テンプレートstruct S {ll val, idx;};struct F {ll x;};S min_op(S l, S r) {if (l.val < r.val) return l;else return r;}S min_e() { return { INF, -1 }; }S max_op(S l, S r) {if (l.val > r.val) return l;else return r;}S max_e() { return { -INF, -1 }; }S mapping(F l, S r) { return { l.x + r.val, r.idx }; }F composition(F l, F r) { return { l.x + r.x }; }F id() { return { 0 }; }S plus_op(S l, S r) {S ans{ l.val + r.val, 0ll };return ans;}S plus_e() { return { 0, -1 }; }//lazy_segtree<S, min_op, min_e, F, mapping, composition, id> seg(n);/*** @brief Fibonacchi-Heap(フィボナッチヒープ)* @see https://www.cs.princeton.edu/~wayne/teaching/fibonacci-heap.pdf*/template< typename key_t, typename val_t >struct FibonacchiHeap {struct Node {key_t key;val_t val;Node* left, * right, * child, * par;int sz;bool mark;Node(const key_t& key, const val_t& val): key(key), val(val), left(this), right(this), par(nullptr), child(nullptr), sz(0), mark(false) {}};Node* root;size_t sz;vector< Node* > rank;FibonacchiHeap() : root(nullptr), sz(0) {}size_t size() const {return sz;}bool empty() const {return sz == 0;}void update_min(Node* t) {if (!root || t->key < root->key) {root = t;}}void concat(Node*& r, Node* t) {if (!r) {r = t;}else {t->left->right = r->right;r->right->left = t->left;t->left = r;r->right = t;}}void delete_node(Node* t) {t->left->right = t->right;t->right->left = t->left;t->left = t;t->right = t;}Node* push(const key_t& key, const val_t& val) {++sz;auto node = new Node(key, val);concat(root, node);update_min(node);return node;}Node* consolidate(Node* s, Node* t) {if (root == s || s->key < t->key) {delete_node(t);++s->sz;t->par = s;concat(s->child, t);return s;}else {delete_node(s);++t->sz;s->par = t;concat(t->child, s);return t;}}pair< key_t, val_t > pop() {--sz;Node* rem = root;auto ret = make_pair(rem->key, rem->val);{root = root->left == root ? nullptr : root->left;delete_node(rem);}if (rem->child) {concat(root, rem->child);}if (root) {{Node* base = root, * cur = base;do {cur->par = nullptr;update_min(cur);cur = cur->right;} while (cur != base);}{Node* base = root;int last = -1;do {Node* nxt = base->right;while (base->sz < rank.size() && rank[base->sz]) {Node* u = rank[base->sz];rank[base->sz] = nullptr;base = consolidate(u, base);}if (base->sz >= rank.size()) rank.resize(base->sz + 1);last = max(last, base->sz);rank[base->sz] = base;base = nxt;} while (base != root);for (int i = last; i >= 0; i--) rank[i] = nullptr;}}return ret;}inline void mark_dfs(Node* t) {if (!t->par) {t->mark = false;}else if (t->mark) {mark_dfs(t->par);t->par->child = t->left == t ? nullptr : t->left;delete_node(t);t->sz--;t->mark = false;t->par = nullptr;concat(root, t);}else {t->mark = true;t->sz--;}}void decrease_key(Node* t, const key_t& d) {t->key -= d;if (!t->par) {update_min(t);return;}if (t->par->key <= t->key) {return;}t->sz++;t->mark = true;mark_dfs(t);update_min(t);}};template< typename T >vector< T > dijkstra_fibonacchi_heap(Graph< T >& g, int s) {const auto INF = numeric_limits< T >::max();using Heap = FibonacchiHeap< T, int >;using Node = typename Heap::Node;Heap heap;vector< Node* > keep(g.size(), nullptr);vector< T > dist;dist.assign(g.size(), INF);dist[s] = 0;keep[s] = heap.push(dist[s], s);while (!heap.empty()) {T cost;int idx;tie(cost, idx) = heap.pop();if (dist[idx] < cost) continue;for (auto& e : g[idx]) {auto next_cost = cost + e.cost;if (dist[e.to] <= next_cost) continue;if (keep[e.to] == nullptr) {dist[e.to] = next_cost;keep[e.to] = heap.push(dist[e.to], e.to);}else {T d = dist[e.to] - next_cost;heap.decrease_key(keep[e.to], d);dist[e.to] -= d;}}}return dist;}int main() {ll n, m;cin >> n >> m;Graph<ll> G(n), Ginv(n);rep(i, m) {ll u, v, t;cin >> u >> v >> t;u--, v--;G.add_directed_edge(u, v, t);Ginv.add_directed_edge(v, u, t);}auto dn2 = dijkstra_fibonacchi_heap(G, n - 2);auto dn1 = dijkstra_fibonacchi_heap(G, n - 1);auto dn2inv = dijkstra_fibonacchi_heap(Ginv, n - 2);auto dn1inv = dijkstra_fibonacchi_heap(Ginv, n - 1);rep(i, n - 2) {ll ans = INF;if (dn2inv[i] != LLONG_MAX && dn2[n-1] != LLONG_MAX&& dn1[i] != LLONG_MAX) chmin(ans, dn2inv[i] + dn2[n - 1] + dn1[i]);if (dn1inv[i] != LLONG_MAX && dn1[n - 2] != LLONG_MAX && dn2[i] != LLONG_MAX) chmin(ans, dn1inv[i] + dn1[n - 2] + dn2[i]);if (ans == INF) ans = -1;print(ans);}}