結果
問題 | No.612 Move on grid |
ユーザー |
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提出日時 | 2020-07-11 04:10:35 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 199 ms / 2,500 ms |
コード長 | 18,251 bytes |
コンパイル時間 | 3,345 ms |
コンパイル使用メモリ | 227,416 KB |
最終ジャッジ日時 | 2025-01-11 19:27:29 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 17 |
ソースコード
#define _USE_MATH_DEFINES#include <bits/stdc++.h>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()using ll = long long;template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;const int INF = 0x3f3f3f3f;const ll LINF = 0x3f3f3f3f3f3f3f3fLL;const double EPS = 1e-8;const int MOD = 1000000007;// const int MOD = 998244353;const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }struct IOSetup {IOSetup() {cin.tie(nullptr);ios_base::sync_with_stdio(false);cout << fixed << setprecision(20);}} iosetup;int mod = MOD;struct ModInt {unsigned val;ModInt(): val(0) {}ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}ModInt pow(ll exponent) {ModInt tmp = *this, res = 1;while (exponent > 0) {if (exponent & 1) res *= tmp;tmp *= tmp;exponent >>= 1;}return res;}ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }ModInt &operator/=(const ModInt &x) {// assert(__gcd(static_cast<int>(x.val), mod) == 1);unsigned a = x.val, b = mod; int u = 1, v = 0;while (b) {unsigned tmp = a / b;swap(a -= tmp * b, b);swap(u -= tmp * v, v);}return *this *= u;}bool operator==(const ModInt &x) const { return val == x.val; }bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; }bool operator<=(const ModInt &x) const { return val <= x.val; }bool operator>(const ModInt &x) const { return val > x.val; }bool operator>=(const ModInt &x) const { return val >= x.val; }ModInt &operator++() { if (++val == mod) val = 0; return *this; }ModInt operator++(int) { ModInt res = *this; ++*this; return res; }ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }ModInt operator--(int) { ModInt res = *this; --*this; return res; }ModInt operator+() const { return *this; }ModInt operator-() const { return ModInt(val ? mod - val : 0); }ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }};ModInt abs(const ModInt &x) { return x; }struct Combinatorics {int val; // "val!" and "mod" must be disjoint.vector<ModInt> fact, fact_inv, inv;Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {fact[0] = 1;FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;fact_inv[val] = ModInt(1) / fact[val];for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];}ModInt nCk(int n, int k) {if (n < 0 || n < k || k < 0) return ModInt(0);// assert(n <= val && k <= val);return fact[n] * fact_inv[k] * fact_inv[n - k];}ModInt nPk(int n, int k) {if (n < 0 || n < k || k < 0) return ModInt(0);// assert(n <= val);return fact[n] * fact_inv[n - k];}ModInt nHk(int n, int k) {if (n < 0 || k < 0) return ModInt(0);return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));}};template <typename T>function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {int n = a.size(), m = b.size();vector<T> res(n + m - 1, T(0));REP(i, n) REP(j, m) res[i + j] += a[i] * b[j];return res;};template <typename T>function<bool(const T&, T&)> sqr = [](const T &a, T &res) {res = T(sqrt(a));return true;};template <typename T>struct FPS {vector<T> co;FPS(int deg = 0) : co(deg + 1, T(0)) {}FPS(const vector<T> &co) : co(co) {}FPS(initializer_list<T> init) : co(init.begin(), init.end()) {}template <typename InputIter> FPS(InputIter first, InputIter last) : co(first, last) {}inline const T &operator[](int term) const { return co[term]; }inline T &operator[](int term) { return co[term]; }void resize(int deg) {int prev = co.size();co.resize(deg + 1);if (prev < deg + 1) fill(co.begin() + prev, co.end(), T(0));}void shrink() { while (co.size() > 1 && co.back() == T(0)) co.pop_back(); }int degree() const { return static_cast<int>(co.size()) - 1; }FPS &operator=(const vector<T> &new_co) {co.resize(new_co.size());copy(ALL(new_co), co.begin());return *this;}FPS &operator=(const FPS &x) {co.resize(x.co.size());copy(ALL(x.co), co.begin());return *this;}FPS &operator+=(const FPS &x) {int n = x.co.size();if (n > co.size()) resize(n - 1);REP(i, n) co[i] += x.co[i];return *this;}FPS &operator-=(const FPS &x) {int n = x.co.size();if (n > co.size()) resize(n - 1);REP(i, n) co[i] -= x.co[i];return *this;}FPS &operator*=(T x) {for (T &e : co) e *= x;return *this;}FPS &operator*=(const FPS &x) { return *this = mul<T>(co, x.co); }FPS &operator/=(T x) {assert(x != T(0));T inv_x = T(1) / x;for (T &e : co) e *= inv_x;return *this;}FPS &operator/=(const FPS &x) {if (x.co.size() > co.size()) return *this = FPS();int n = co.size() - x.co.size() + 1;FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + min(static_cast<int>(x.co.size()), n));b = b.inv(n - 1);a *= b;return *this = FPS(a.co.rend() - n, a.co.rend());}FPS &operator%=(const FPS &x) {*this -= *this / x * x;co.resize(static_cast<int>(x.co.size()) - 1);if (co.empty()) co = {T(0)};return *this;}FPS &operator<<=(int n) {co.insert(co.begin(), n, T(0));return *this;}FPS &operator>>=(int n) {if (co.size() < n) return *this = FPS();co.erase(co.begin(), co.begin() + n);return *this;}bool operator==(const FPS &x) const {FPS a(*this), b(x);a.shrink(); b.shrink();int n = a.co.size();if (n != b.co.size()) return false;REP(i, n) if (a.co[i] != b.co[i]) return false;return true;}bool operator!=(const FPS &x) const { return !(*this == x); }FPS operator+() const { return *this; }FPS operator-() const {FPS res(*this);for (T &e : res.co) e = T(-e);return res;}FPS operator+(const FPS &x) const { return FPS(*this) += x; }FPS operator-(const FPS &x) const { return FPS(*this) -= x; }FPS operator*(T x) const { return FPS(*this) *= x; }FPS operator*(const FPS &x) const { return FPS(*this) *= x; }FPS operator/(T x) const { return FPS(*this) /= x; }FPS operator/(const FPS &x) const { return FPS(*this) /= x; }FPS operator%(const FPS &x) const { return FPS(*this) %= x; }FPS operator<<(int n) const { return FPS(*this) <<= n; }FPS operator>>(int n) const { return FPS(*this) >>= n; }T horner(T val) const {T res = T(0);for (int i = static_cast<int>(co.size()) - 1; i >= 0; --i) (res *= val) += co[i];return res;}FPS differential() const {int n = co.size();assert(n >= 1);FPS res(n - 1);FOR(i, 1, n) res.co[i - 1] = co[i] * T(i);return res;}FPS integral() const {int n = co.size();FPS res(n + 1);REP(i, n) res[i + 1] = co[i] / T(i + 1);return res;}FPS exp(int deg = -1) const {assert(co[0] == T(0));if (deg == -1) deg = static_cast<int>(co.size()) - 1;FPS one({T(1)}), res = one;for (int i = 1; i <= deg; i <<= 1) {res *= FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) - res.log((i << 1) - 1) + one;res.co.resize(i << 1);}res.co.resize(deg + 1);return res;}FPS inv(int deg = -1) const {assert(co[0] != T(0));if (deg == -1) deg = static_cast<int>(co.size()) - 1;FPS res({T(1) / co[0]});for (int i = 1; i <= deg; i <<= 1) {res = res + res - res * res * FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1));res.co.resize(i << 1);}res.co.resize(deg + 1);return res;}FPS log(int deg = -1) const {assert(co[0] == T(1));if (deg == -1) deg = static_cast<int>(co.size()) - 1;FPS integrand = differential() * inv(deg - 1);integrand.co.resize(deg);return integrand.integral();}FPS pow(ll exponent, int deg = -1) const {int n = co.size();if (deg == -1) deg = n - 1;REP(i, n) {if (co[i] != T(0)) {ll shift = exponent * i;if (shift > deg) break;T tmp = 1, base = co[i];ll e = exponent;while (e > 0) {if (e & 1) tmp *= base;base *= base;e >>= 1;}return ((((*this >> i) * (T(1) / co[i])).log(deg - shift) * T(exponent)).exp(deg - shift) * tmp) << shift;}}return FPS(deg);}FPS mod_pow(ll exponent, const FPS &md) const {FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv();int deg_of_md = md.co.size();function<void(FPS&, const FPS&)> mod_mul = [&](FPS &multiplicand, const FPS &multiplier) {multiplicand *= multiplier;if (deg_of_md <= multiplicand.co.size()) {int n = multiplicand.co.size() - deg_of_md + 1;FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + min(static_cast<int>(inv_rev_md.co.size()), n));multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md;}multiplicand.co.resize(deg_of_md - 1);if (multiplicand.co.empty()) multiplicand.co = {T(0)};};FPS res({T(1)}), base = *this;mod_mul(base, res);while (exponent > 0) {if (exponent & 1) mod_mul(res, base);mod_mul(base, base);exponent >>= 1;}return res;}FPS sqrt(int deg = -1) const {int n = co.size();if (deg == -1) deg = n - 1;if (co[0] == T(0)) {FOR(i, 1, n) {if (co[i] == T(0)) continue;if (i & 1) return FPS(-1);int shift = i >> 1;if (deg < shift) break;FPS res = (*this >> i).sqrt(deg - shift);if (res.co.empty()) return FPS(-1);res <<= shift;res.resize(deg);return res;}return FPS(deg);}T s;if (!sqr<T>(co[0], s)) return FPS(-1);FPS res({s});T half = T(1) / T(2);for (int i = 1; i <= deg; i <<= 1) {(res += FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) * res.inv((i << 1) - 1)) *= half;}res.resize(deg);return res;}FPS translate(T c) const {int n = co.size();vector<T> fact(n, T(1)), inv_fact(n, T(1));FOR(i, 1, n) fact[i] = fact[i - 1] * T(i);inv_fact[n - 1] = T(1) / fact[n - 1];for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * T(i);vector<T> g(n), ex(n);REP(i, n) g[n - 1 - i] = co[i] * fact[i];T pow_c = T(1);REP(i, n) {ex[i] = pow_c * inv_fact[i];pow_c *= c;}vector<T> conv = mul<T>(g, ex);FPS res(n - 1);REP(i, n) res[i] = conv[n - 1 - i] * inv_fact[i];return res;}};namespace FFT {using Real = double;struct Complex {Real re, im;Complex(Real re = 0, Real im = 0) : re(re), im(im) {}inline Complex operator+(const Complex &x) const { return Complex(re + x.re, im + x.im); }inline Complex operator-(const Complex &x) const { return Complex(re - x.re, im - x.im); }inline Complex operator*(const Complex &x) const { return Complex(re * x.re - im * x.im, re * x.im + im * x.re); }inline Complex mul_real(Real r) const { return Complex(re * r, im * r); }inline Complex mul_pin(Real r) const { return Complex(-im * r, re * r); }inline Complex conj() const { return Complex(re, -im); }};vector<int> butterfly{0};vector<vector<Complex> > zeta{{{1, 0}}};void calc(int n) {int prev_n = butterfly.size();if (n <= prev_n) return;butterfly.resize(n);int prev_lg = zeta.size(), lg = __builtin_ctz(n);FOR(i, 1, prev_n) butterfly[i] <<= lg - prev_lg;FOR(i, prev_n, n) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));zeta.resize(lg);FOR(i, prev_lg, lg) {zeta[i].resize(1 << i);Real angle = -M_PI * 2 / (1 << (i + 1));REP(j, 1 << (i - 1)) {zeta[i][j << 1] = zeta[i - 1][j];Real theta = angle * ((j << 1) + 1);zeta[i][(j << 1) + 1] = {cos(theta), sin(theta)};}}}void sub_dft(vector<Complex> &a) {int n = a.size();// assert(__builtin_popcount(n) == 1);calc(n);int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);REP(i, n) {int j = butterfly[i] >> shift;if (i < j) swap(a[i], a[j]);}for (int block = 1; block < n; block <<= 1) {int den = __builtin_ctz(block);for (int i = 0; i < n; i += (block << 1)) REP(j, block) {Complex tmp = a[i + j + block] * zeta[den][j];a[i + j + block] = a[i + j] - tmp;a[i + j] = a[i + j] + tmp;}}}template <typename T>vector<Complex> dft(const vector<T> &a) {int sz = a.size(), lg = 1;while ((1 << lg) < sz) ++lg;vector<Complex> c(1 << lg);REP(i, sz) c[i].re = a[i];sub_dft(c);return c;}vector<Real> real_idft(vector<Complex> &a) {int n = a.size(), half = n >> 1, quarter = half >> 1;// assert(__builtin_popcount(n) == 1);calc(n);a[0] = (a[0] + a[half] + (a[0] - a[half]).mul_pin(1)).mul_real(0.5);int den = __builtin_ctz(half);FOR(i, 1, quarter) {int j = half - i;Complex tmp1 = a[i] + a[j].conj(), tmp2 = ((a[i] - a[j].conj()) * zeta[den][j]).mul_pin(1);a[i] = (tmp1 - tmp2).mul_real(0.5);a[j] = (tmp1 + tmp2).mul_real(0.5).conj();}if (quarter > 0) a[quarter] = a[quarter].conj();a.resize(half);sub_dft(a);reverse(a.begin() + 1, a.end());Real r = 1.0 / half;vector<Real> res(n);REP(i, n) res[i] = (i & 1 ? a[i >> 1].im : a[i >> 1].re) * r;return res;}void idft(vector<Complex> &a) {int n = a.size();sub_dft(a);reverse(a.begin() + 1, a.end());Real r = 1.0 / n;REP(i, n) a[i] = a[i].mul_real(r);}template <typename T>vector<Real> convolution(const vector<T> &a, const vector<T> &b) {int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;while ((1 << lg) < sz) ++lg;int n = 1 << lg;vector<Complex> c(n);REP(i, a_sz) c[i].re = a[i];REP(i, b_sz) c[i].im = b[i];sub_dft(c);int half = n >> 1;c[0] = Complex(c[0].re * c[0].im, 0);FOR(i, 1, half) {Complex i_square = c[i] * c[i], j_square = c[n - i] * c[n - i];c[i] = (j_square.conj() - i_square).mul_pin(0.25);c[n - i] = (i_square.conj() - j_square).mul_pin(0.25);}c[half] = Complex(c[half].re * c[half].im, 0);vector<Real> res = real_idft(c);res.resize(sz);return res;}};vector<ModInt> mod_convolution(const vector<ModInt> &a, const vector<ModInt> &b, const int pre = 15) {using Complex = FFT::Complex;int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;while ((1 << lg) < sz) ++lg;int n = 1 << lg;vector<Complex> A(n), B(n);REP(i, a_sz) {int ai = a[i].val;A[i] = Complex(ai & ((1 << pre) - 1), ai >> pre);}REP(i, b_sz) {int bi = b[i].val;B[i] = Complex(bi & ((1 << pre) - 1), bi >> pre);}FFT::sub_dft(A);FFT::sub_dft(B);int half = n >> 1;Complex tmp_a = A[0], tmp_b = B[0];A[0] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im};B[0] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0};FOR(i, 1, half) {int j = n - i;Complex a_l_i = (A[i] + A[j].conj()).mul_real(0.5), a_h_i = (A[j].conj() - A[i]).mul_pin(0.5);Complex b_l_i = (B[i] + B[j].conj()).mul_real(0.5), b_h_i = (B[j].conj() - B[i]).mul_pin(0.5);Complex a_l_j = (A[j] + A[i].conj()).mul_real(0.5), a_h_j = (A[i].conj() - A[j]).mul_pin(0.5);Complex b_l_j = (B[j] + B[i].conj()).mul_real(0.5), b_h_j = (B[i].conj() - B[j]).mul_pin(0.5);A[i] = a_l_i * b_l_i + (a_h_i * b_h_i).mul_pin(1);B[i] = a_l_i * b_h_i + a_h_i * b_l_i;A[j] = a_l_j * b_l_j + (a_h_j * b_h_j).mul_pin(1);B[j] = a_l_j * b_h_j + a_h_j * b_l_j;}tmp_a = A[half]; tmp_b = B[half];A[half] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im};B[half] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0};FFT::idft(A);FFT::idft(B);vector<ModInt> res(sz);ModInt tmp1 = 1 << pre, tmp2 = 1LL << (pre << 1);REP(i, sz) {res[i] += static_cast<ll>(A[i].re + 0.5);res[i] += tmp1 * static_cast<ll>(B[i].re + 0.5);res[i] += tmp2 * static_cast<ll>(A[i].im + 0.5);}return res;}int main() {mul<ModInt> = [&](const vector<ModInt> &a, const vector<ModInt> &b) {return mod_convolution(a, b);};const int N = 20000;int t, a, b, c, d, e; cin >> t >> a >> b >> c >> d >> e;int geta = max({abs(a), abs(b), abs(c)});FPS<ModInt> fps(N);fps[geta + a] += 1;fps[geta - a] += 1;fps[geta + b] += 1;fps[geta - b] += 1;fps[geta + c] += 1;fps[geta - c] += 1;fps = fps.pow(t, N);geta *= t;ModInt ans = 0;FOR(i, max(geta + d, 0), geta + e + 1) ans += fps[i];cout << ans << '\n';return 0;}