結果
| 問題 |
No.2595 Parsing Challenge
|
| コンテスト | |
| ユーザー |
 tko919
|
| 提出日時 | 2023-12-23 12:01:56 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 47,067 bytes |
| コンパイル時間 | 3,663 ms |
| コンパイル使用メモリ | 246,616 KB |
| 最終ジャッジ日時 | 2025-02-18 13:46:29 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 52 TLE * 1 -- * 2 |
ソースコード
#line 1 "sol.cpp"
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using ll = long long int;
using ull = unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) { return __builtin_popcountll(x); }
template <typename T> int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
class FastIO {
static constexpr int L = 1 << 16;
char rdbuf[L];
int rdLeft = 0, rdRight = 0;
inline void reload() {
int len = rdRight - rdLeft;
memmove(rdbuf, rdbuf + rdLeft, len);
rdLeft = 0, rdRight = len;
rdRight += fread(rdbuf + len, 1, L - len, stdin);
}
inline bool skip() {
for (;;) {
while (rdLeft != rdRight and rdbuf[rdLeft] <= ' ')
rdLeft++;
if (rdLeft == rdRight) {
reload();
if (rdLeft == rdRight)
return false;
} else
break;
}
return true;
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
inline bool _read(T &x) {
if (!skip())
return false;
if (rdLeft + 20 >= rdRight)
reload();
bool neg = false;
if (rdbuf[rdLeft] == '-') {
neg = true;
rdLeft++;
}
x = 0;
while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
x = x * 10 +
(neg ? -(rdbuf[rdLeft++] ^ 48) : (rdbuf[rdLeft++] ^ 48));
}
return true;
}
inline bool _read(__int128_t &x) {
if (!skip())
return false;
if (rdLeft + 40 >= rdRight)
reload();
bool neg = false;
if (rdbuf[rdLeft] == '-') {
neg = true;
rdLeft++;
}
x = 0;
while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
x = x * 10 +
(neg ? -(rdbuf[rdLeft++] ^ 48) : (rdbuf[rdLeft++] ^ 48));
}
return true;
}
inline bool _read(__uint128_t &x) {
if (!skip())
return false;
if (rdLeft + 40 >= rdRight)
reload();
x = 0;
while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
x = x * 10 + (rdbuf[rdLeft++] ^ 48);
}
return true;
}
template <typename T, enable_if_t<is_floating_point<T>::value, int> = 0>
inline bool _read(T &x) {
if (!skip())
return false;
if (rdLeft + 20 >= rdRight)
reload();
bool neg = false;
if (rdbuf[rdLeft] == '-') {
neg = true;
rdLeft++;
}
x = 0;
while (rdbuf[rdLeft] >= '0' and rdbuf[rdLeft] <= '9' and
rdLeft < rdRight) {
x = x * 10 + (rdbuf[rdLeft++] ^ 48);
}
if (rdbuf[rdLeft] != '.')
return true;
rdLeft++;
T base = .1;
while (rdbuf[rdLeft] >= '0' and rdbuf[rdLeft] <= '9' and
rdLeft < rdRight) {
x += base * (rdbuf[rdLeft++] ^ 48);
base *= .1;
}
if (neg)
x = -x;
return true;
}
inline bool _read(char &x) {
if (!skip())
return false;
if (rdLeft + 1 >= rdRight)
reload();
x = rdbuf[rdLeft++];
return true;
}
inline bool _read(string &x) {
if (!skip())
return false;
for (;;) {
int pos = rdLeft;
while (pos < rdRight and rdbuf[pos] > ' ')
pos++;
x.append(rdbuf + rdLeft, pos - rdLeft);
if (rdLeft == pos)
break;
rdLeft = pos;
if (rdLeft == rdRight)
reload();
else
break;
}
return true;
}
template <typename T> inline bool _read(vector<T> &v) {
for (auto &x : v) {
if (!_read(x))
return false;
}
return true;
}
char wtbuf[L], tmp[50];
int wtRight = 0;
inline void _write(const char &x) {
if (wtRight > L - 32)
flush();
wtbuf[wtRight++] = x;
}
inline void _write(const string &x) {
for (auto &c : x)
_write(c);
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
inline void _write(T x) {
if (wtRight > L - 32)
flush();
if (x == 0) {
_write('0');
return;
} else if (x < 0) {
_write('-');
if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
switch (sizeof(x)) {
case 2:
_write("32768");
return;
case 4:
_write("2147483648");
return;
case 8:
_write("9223372036854775808");
return;
}
}
x = -x;
}
int pos = 0;
while (x != 0) {
tmp[pos++] = char((x % 10) | 48);
x /= 10;
}
rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
wtRight += pos;
}
inline void _write(__int128_t x) {
if (wtRight > L - 40)
flush();
if (x == 0) {
_write('0');
return;
} else if (x < 0) {
_write('-');
x = -x;
}
int pos = 0;
while (x != 0) {
tmp[pos++] = char((x % 10) | 48);
x /= 10;
}
rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
wtRight += pos;
}
inline void _write(__uint128_t x) {
if (wtRight > L - 40)
flush();
if (x == 0) {
_write('0');
return;
}
int pos = 0;
while (x != 0) {
tmp[pos++] = char((x % 10) | 48);
x /= 10;
}
rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
wtRight += pos;
}
inline void _write(double x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
_write(s);
}
template <typename T> inline void _write(const vector<T> &v) {
rep(i, 0, v.size()) {
if (i)
_write(' ');
_write(v[i]);
}
}
public:
FastIO() {}
~FastIO() { flush(); }
inline void read() {}
template <typename Head, typename... Tail>
inline void read(Head &head, Tail &...tail) {
assert(_read(head));
read(tail...);
}
template <bool ln = true, bool space = false> inline void write() {
if (ln)
_write('\n');
}
template <bool ln = true, bool space = false, typename Head,
typename... Tail>
inline void write(const Head &head, const Tail &...tail) {
_write(head);
write<ln, true>(tail...);
if (space)
_write(' ');
}
inline void flush() {
fwrite(wtbuf, 1, wtRight, stdout);
wtRight = 0;
}
};
/**
* @brief Fast IO
*/
#line 310 "sol.cpp"
#ifndef ATCODER_CONVOLUTION_HPP
#define ATCODER_CONVOLUTION_HPP 1
#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#endif
#if __cplusplus >= 202002L
#include <bit>
#endif
namespace atcoder {
namespace internal {
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n))
x *= 2;
return x;
}
#endif
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x)))
x++;
return x;
}
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_BITOP_HPP#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0)
x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m)
: _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1)
// < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
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);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0)
m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_MATH_HPP#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_VER
template <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;
#else
template <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;
#endif
template <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;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP
namespace 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>;
} // namespace internal
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());
}
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());
}
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>;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
template <class mint, int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint> * = nullptr>
struct fft_info {
static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[countr_zero(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[countr_zero(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 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()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[countr_zero(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[countr_zero(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint> &a,
const std::vector<mint> &b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = (int)internal::bit_ceil((unsigned int)(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;
}
} // namespace internal
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 {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n, m) <= 60)
return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(const std::vector<mint> &a,
const std::vector<mint> &b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m)
return {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n, m) <= 60)
return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
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>;
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
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(std::move(a2), std::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; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
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;
static constexpr int MAX_AB_BIT = 24;
static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1,
"MOD1 isn't enough to support an array length of 2^24.");
static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1,
"MOD2 isn't enough to support an array length of 2^24.");
static_assert(MOD3 % (1ull << MAX_AB_BIT) == 1,
"MOD3 isn't enough to support an array length of 2^24.");
assert(n + m - 1 <= (1 << MAX_AB_BIT));
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;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
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;
}
} // namespace atcoder
const int DIGIT = 6;
const int BASE = 1000000;
struct positive_bigint {
std::vector<int> d;
positive_bigint() {}
positive_bigint(long long X) {
while (X > 0) {
d.push_back(X % BASE);
X /= BASE;
}
}
positive_bigint(std::string S) {
if (S == "0") {
S = "";
}
int L = S.size();
d.resize((L + DIGIT - 1) / DIGIT, 0);
for (int i = L - 1; i >= 0; i -= 6) {
for (int j = std::max(i - 5, 0); j <= i; j++) {
d[i / DIGIT] *= 10;
d[i / DIGIT] += S[j] - '0';
}
}
std::reverse(d.begin(), d.end());
}
bool empty() const { return d.empty(); }
int size() const { return d.size(); }
int &operator[](int i) { return d[i]; }
int operator[](int i) const { return d[i]; }
};
std::string to_string(const positive_bigint &A) {
int N = A.size();
std::string ans;
for (int i = N - 1; i >= 0; i--) {
std::string tmp = std::to_string(A[i]);
if (i < N - 1) {
ans += std::string(DIGIT - tmp.size(), '0');
}
ans += tmp;
}
if (ans.empty()) {
ans = "0";
}
return ans;
}
std::istream &operator>>(std::istream &is, positive_bigint &A) {
std::string S;
is >> S;
A = positive_bigint(S);
return is;
}
std::ostream &operator<<(std::ostream &os, positive_bigint &A) {
os << to_string(A);
return os;
}
int cmp(const positive_bigint &A, const positive_bigint &B) {
int N = A.size();
int M = B.size();
if (N < M) {
return -1;
} else if (N > M) {
return 1;
} else {
for (int i = N - 1; i >= 0; i--) {
if (A[i] < B[i]) {
return -1;
}
if (A[i] > B[i]) {
return 1;
}
}
return 0;
}
}
bool operator==(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) == 0;
}
bool operator!=(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) != 0;
}
bool operator<(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) < 0;
}
bool operator>(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) > 0;
}
bool operator<=(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) <= 0;
}
bool operator>=(const positive_bigint &A, const positive_bigint &B) {
return cmp(A, B) >= 0;
}
positive_bigint &operator+=(positive_bigint &A, const positive_bigint &B) {
int N = A.size();
int M = B.size();
while (N < M) {
A.d.push_back(0);
N++;
}
for (int i = 0; i < M; i++) {
A[i] += B[i];
}
for (int i = 0; i < N - 1; i++) {
if (A[i] >= BASE) {
A[i] -= BASE;
A[i + 1]++;
}
}
if (N > 0) {
if (A[N - 1] >= BASE) {
A.d.push_back(1);
A[N - 1] -= BASE;
}
}
return A;
}
positive_bigint operator+(const positive_bigint &A, const positive_bigint &B) {
positive_bigint A2 = A;
A2 += B;
return A2;
}
positive_bigint &operator-=(positive_bigint &A, const positive_bigint &B) {
int N = A.size();
int M = B.size();
for (int i = 0; i < M; i++) {
A[i] -= B[i];
}
for (int i = 0; i < N - 1; i++) {
if (A[i] < 0) {
A[i] += BASE;
A[i + 1]--;
}
}
while (!A.empty()) {
if (A.d.back() == 0) {
A.d.pop_back();
} else {
break;
}
}
return A;
}
positive_bigint operator-(const positive_bigint &A, const positive_bigint &B) {
positive_bigint A2 = A;
A2 -= B;
return A2;
}
positive_bigint operator*(const positive_bigint &A, const positive_bigint &B) {
if (A.empty() || B.empty()) {
return 0;
}
int N = A.size();
int M = B.size();
std::vector<long long> a(N);
for (int i = 0; i < N; i++) {
a[i] = A[i];
}
std::vector<long long> b(M);
for (int i = 0; i < M; i++) {
b[i] = B[i];
}
std::vector<long long> C = atcoder::convolution_ll(a, b);
for (int i = 0; i < N + M - 2; i++) {
C[i + 1] += C[i] / BASE;
C[i] %= BASE;
}
if (C[N + M - 2] >= BASE) {
C.resize(N + M);
C[N + M - 1] += C[N + M - 2] / BASE;
C[N + M - 2] %= BASE;
}
positive_bigint ans;
ans.d.resize(C.size());
for (int i = 0; i < C.size(); i++) {
ans[i] = C[i];
}
return ans;
}
positive_bigint operator*=(positive_bigint &A, const positive_bigint &B) {
A = A * B;
return A;
}
struct bigint {
bool neg = false;
positive_bigint a;
bigint() {}
bigint(long long X) : neg(X < 0), a(abs(X)) {}
bigint(const positive_bigint &X, bool neg = false) : neg(neg), a(X) {}
bigint(const std::string &s) {
if (!s.empty()) {
if (s[0] == '-') {
neg = true;
a = positive_bigint(s.substr(1, s.size() - 1));
} else {
a = positive_bigint(s);
}
}
}
bool empty() const { return a.empty(); }
int size() const { return a.size(); }
int &operator[](int i) { return a[i]; }
};
std::string to_string(const bigint &A) {
std::string ans;
if (A.neg) {
ans += '-';
}
ans += to_string(A.a);
return ans;
}
std::istream &operator>>(std::istream &is, bigint &A) {
std::string S;
is >> S;
if (S != "0") {
A = bigint(S);
}
return is;
}
std::ostream &operator<<(std::ostream &os, bigint A) {
os << to_string(A);
return os;
}
positive_bigint abs(const bigint &A) { return A.a; }
int cmp(const bigint &A, const bigint &B) {
if (!A.neg) {
if (!B.neg) {
return cmp(A.a, B.a);
} else {
return 1;
}
} else {
if (!B.neg) {
return -1;
} else {
return cmp(B.a, A.a);
}
}
}
bool operator==(const bigint &A, const bigint &B) { return cmp(A, B) == 0; }
bool operator!=(const bigint &A, const bigint &B) { return cmp(A, B) != 0; }
bool operator<(const bigint &A, const bigint &B) { return cmp(A, B) < 0; }
bool operator>(const bigint &A, const bigint &B) { return cmp(A, B) > 0; }
bool operator<=(const bigint &A, const bigint &B) { return cmp(A, B) <= 0; }
bool operator>=(const bigint &A, const bigint &B) { return cmp(A, B) >= 0; }
bigint operator+(const bigint &A) { return A; }
bigint operator-(const bigint &A) {
bigint A2 = A;
if (!A2.empty()) {
A2.neg = !A2.neg;
}
return A2;
}
bigint &operator+=(bigint &A, const bigint &B) {
if (A.neg == B.neg) {
A.a += B.a;
} else {
int c = cmp(A.a, B.a);
if (c > 0) {
A.a -= B.a;
} else if (c < 0) {
A.a = B.a - A.a;
A.neg = !A.neg;
} else {
A = 0;
}
}
return A;
}
bigint operator+(const bigint &A, const bigint &B) {
bigint A2 = A;
A2 += B;
return A2;
}
bigint &operator-=(bigint &A, const bigint &B) {
if (A.neg != B.neg) {
A.a += B.a;
} else {
int c = cmp(A.a, B.a);
if (c > 0) {
A.a -= B.a;
} else if (c < 0) {
A.a = B.a - A.a;
A.neg = !A.neg;
} else {
A = 0;
}
}
return A;
}
bigint operator-(const bigint &A, const bigint &B) {
bigint A2 = A;
A2 -= B;
return A2;
}
bigint operator*=(bigint &A, const bigint &B) {
if (A.empty() || B.empty()) {
A = 0;
} else {
if (B.neg) {
A.neg = !A.neg;
}
A.a *= B.a;
}
return A;
}
bigint operator*(const bigint &A, const bigint &B) {
bigint A2 = A;
A2 *= B;
return A2;
}
typedef string::const_iterator State;
void expr(State &beg, bigint &x);
void term(State &beg, bigint &x);
void factor(State &beg, bigint &x);
void num(State &beg, bigint &x);
void expr(State &beg, bigint &x) {
term(beg, x);
bigint buf;
for (;;) {
buf = 0;
if ((*beg) == '+') {
beg++;
term(beg, buf);
x += buf;
} else if ((*beg) == '-') {
beg++;
term(beg, buf);
x -= buf;
} else
break;
}
}
void term(State &beg, bigint &x) {
factor(beg, x);
if((*beg)!='*')return;
deque<bigint> deq;
deq.push_back(x);
bigint buf;
while ((*beg) == '*') {
beg++;
buf = 0;
factor(beg, buf);
deq.push_back(buf);
}
while (deq.size() > 1) {
auto x = deq[0];
deq.pop_front();
auto y = deq[0];
deq.pop_front();
deq.push_back(x * y);
}
x = deq[0];
}
void factor(State &beg, bigint &x) {
if ((*beg) == '(') {
beg++;
expr(beg, x);
beg++;
} else
num(beg, x);
}
void num(State &beg, bigint &x) {
bool neg = 0;
while ((*beg) == '-') {
neg ^= 1;
beg++;
}
string buf;
while (isdigit(*beg)) {
buf += (*beg);
beg++;
}
x = bigint(buf);
if (neg)
x = -x;
}
FastIO io;
int main() {
int n = 1000000;
string s;
//rep(_, 0, n / 3) s += '(';
//rep(_,0,n/3)s += '1';
// rep(_, 0, n / 3) s += ')';
io.read(n, s);
State it = s.begin();
bigint ret;
expr(it, ret);
cout << to_string(ret) << '\n';
return 0;
}