結果
| 問題 | No.2988 Min-Plus Convolution Query |
| ユーザー |
 hotman78
|
| 提出日時 | 2024-12-13 15:14:11 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 33,386 bytes |
| コンパイル時間 | 3,579 ms |
| コンパイル使用メモリ | 244,020 KB |
| 実行使用メモリ | 202,740 KB |
| 最終ジャッジ日時 | 2024-12-13 15:14:53 |
| 合計ジャッジ時間 | 37,199 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
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
6,820 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 1,307 ms
172,988 KB |
| testcase_03 | AC | 1,341 ms
175,864 KB |
| testcase_04 | AC | 1,360 ms
175,348 KB |
| testcase_05 | AC | 126 ms
46,468 KB |
| testcase_06 | AC | 2 ms
6,816 KB |
| testcase_07 | AC | 2 ms
6,820 KB |
| testcase_08 | AC | 3 ms
6,816 KB |
| testcase_09 | AC | 102 ms
18,172 KB |
| testcase_10 | AC | 104 ms
27,508 KB |
| testcase_11 | AC | 24 ms
9,120 KB |
| testcase_12 | AC | 47 ms
7,808 KB |
| testcase_13 | AC | 497 ms
37,840 KB |
| testcase_14 | AC | 57 ms
8,704 KB |
| testcase_15 | AC | 631 ms
62,624 KB |
| testcase_16 | AC | 1,237 ms
164,892 KB |
| testcase_17 | AC | 667 ms
49,852 KB |
| testcase_18 | AC | 592 ms
48,256 KB |
| testcase_19 | AC | 407 ms
41,084 KB |
| testcase_20 | AC | 1,877 ms
183,544 KB |
| testcase_21 | AC | 1,748 ms
172,796 KB |
| testcase_22 | AC | 1,392 ms
175,808 KB |
| testcase_23 | AC | 1,805 ms
177,964 KB |
| testcase_24 | AC | 1,857 ms
197,580 KB |
| testcase_25 | AC | 1,661 ms
173,124 KB |
| testcase_26 | AC | 1,800 ms
202,740 KB |
| testcase_27 | AC | 1,494 ms
176,128 KB |
| testcase_28 | TLE | - |
| testcase_29 | AC | 1,490 ms
176,432 KB |
| testcase_30 | TLE | - |
| testcase_31 | AC | 1,407 ms
175,720 KB |
| testcase_32 | AC | 2 ms
6,820 KB |
| testcase_33 | AC | 2 ms
6,816 KB |
| testcase_34 | AC | 2 ms
6,820 KB |
| testcase_35 | AC | 2 ms
6,816 KB |
| testcase_36 | AC | 2 ms
6,816 KB |
| testcase_37 | AC | 2 ms
6,820 KB |
| testcase_38 | AC | 2 ms
6,816 KB |
| testcase_39 | AC | 2 ms
6,816 KB |
| testcase_40 | AC | 2 ms
6,816 KB |
| testcase_41 | AC | 2 ms
6,816 KB |
ソースコード
// author: hotman78
// date: 2024/12/13-15:13:57
// --- begin raw code -----------------
// #include "cpplib/math/ACL_modint1000000007.hpp"
// #include "cpplib/util/template.hpp"
//
// struct tree {
// vector< lint > b;
// vector< pair< lint, lint > > v;
// lint n;
// vec l, r;
// vector< vector< tuple< lint, lint, lint > > > hist;
// tree(vector< lint > &b): b(b) {
// n = b.size();
// v.resize(b.size() * 4, make_pair(0, INF));
// l.resize(b.size() * 4);
// r.resize(b.size() * 4);
// rep(i, n * 2) {
// l[i + n * 2] = i;
// r[i + n * 2] = i;
// }
// rrep(i, 1, n * 2) {
// l[i] = l[i * 2];
// r[i] = r[i * 2 + 1];
// }
// }
// lint get(lint p, lint x, lint k) {
// if (k - p < 0) {
// return b[0] + (1LL << 40) * (p - k) + x;
// }
// if (k - p >= n) {
// return b.back() + (1LL << 40) * (k - p - n + 1) + x;
// }
// return b[k - p] + x;
// }
// void add(lint p, lint x) {
// lint now = 1;
// hist.emplace_back();
// while (1) {
// lint mid = (l[now] + r[now]) / 2;
// if (get(v[now].first, v[now].second, mid) >
// get(p, x, mid)) {
// lint s = v[now].first;
// lint t = v[now].second;
// hist.back().emplace_back(now, s, t);
// v[now] = make_pair(p, x);
// p = s;
// x = t;
// }
// // cerr << now << " " << n << endl;
// if (now >= n * 2) {
// break;
// }
// if (get(v[now].first, v[now].second, l[now]) >
// get(p, x, l[now])) {
// now = now * 2;
// } else if (get(v[now].first, v[now].second, r[now]) >
// get(p, x, r[now])) {
// now = now * 2 + 1;
// } else {
// break;
// }
// }
// }
// lint query(lint k) {
// lint now = 1;
// lint res = INF;
// while (1) {
// chmin(res, get(v[now].first, v[now].second, k));
// if (now >= n * 2) break;
// if (l[now * 2] <= k && k <= r[now * 2]) {
// now = now * 2;
// } else {
// now = now * 2 + 1;
// }
// }
// return res;
// }
// void rollback() {
// while (hist.back().size()) {
// auto [now, s, t] = hist.back().back();
// hist.back().pop_back();
// v[now] = make_pair(s, t);
// }
// hist.pop_back();
// }
// };
// void solve() {
// lint n, q;
// cin >> n >> q;
// vector< lint > a(n);
// vector< lint > b(n);
// rep(i, n) cin >> a[i];
// rep(i, n) cin >> b[i];
// lint cnt = 1;
// while (n & (n - 1)) {
// ++n;
// a.emplace_back(INF);
// b.emplace_back((1LL << 40) * cnt);
// ++cnt;
// }
// tree t(b);
// lint sz = q;
// while (sz & (sz - 1)) sz++;
// vector< vector< pair< lint, lint > > > v(sz * 2);
// // rep(i, n) {
// // t.add(i, a[i]);
// // }
// vector< lint > qk(q);
// vector< vector< pair< lint, lint > > > idx(n);
// rep(i, q) {
// lint p, x, k;
// cin >> p >> x >> k;
// --p;
// k -= 2;
// qk[i] = k;
// if (i == 0) {
// a[p] = x;
// rep(j, n) {
// idx[j].emplace_back(0, a[j]);
// }
// continue;
// } else {
// idx[p].emplace_back(i, x);
// }
// }
// rep(i, n) {
// idx[i].emplace_back(q, -1);
// }
// // debug2(idx);
// rep(i, n) {
// if (a[i] == INF) continue;
// rep(j, idx[i].size() - 1) {
// lint l = idx[i][j].first;
// lint r = idx[i][j + 1].first;
// lint x = idx[i][j].second;
// lint now = 1, s = 0, t = sz;
// auto dfs = [&](auto dfs, lint now, lint s, lint t) {
// if (l <= s && t <= r) {
// v[now].emplace_back(i, x);
// return;
// }
// lint mid = (s + t) / 2;
// // [s,mid) と [l,r) が交差している
// if (l < mid && s < r) {
// dfs(dfs, now * 2, s, mid);
// }
// if (l < t && mid < r) {
// dfs(dfs, now * 2 + 1, mid, t);
// }
// };
// dfs(dfs, now, s, t);
// }
// }
// auto dfs = [&](auto dfs, lint now) -> void {
// for (auto [i, x]: v[now]) {
// t.add(i, x);
// }
// if (now >= sz) {
// if (now - sz < qk.size()) {
// cout << t.query(qk[now - sz]) << endl;
// }
// }
// if (now < sz) {
// dfs(dfs, now * 2);
// dfs(dfs, now * 2 + 1);
// }
// rep(i, v[now].size()) {
// t.rollback();
// }
// };
// // cerr << t.hist.size() << endl;
// dfs(dfs, 1);
// // cerr << t.hist.size() << endl;
// }
// int main() {
// solve();
// // lint t;cin>>t;while(t--)solve();
// }
// --- end raw code -----------------
#line 2 "cpplib/math/ACL_modint1000000007.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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;
explicit 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_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned 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;
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);
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; // |m1 * u| <= |m1| * s <= b
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;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#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
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
using mint = atcoder::modint1000000007;
#line 2 "cpplib/math/ACL_modint_base.hpp"
#include <fstream>
#include <vector>
std::ostream &operator<<(std::ostream &lhs, const mint &rhs) noexcept {
lhs << rhs.val();
return lhs;
}
std::istream &operator>>(std::istream &lhs, mint &rhs) noexcept {
long long x;
lhs >> x;
rhs = x;
return lhs;
}
int MOD_NOW = -1;
int FACT_TABLE_SIZE = 0;
std::vector<mint> fact_table, fact_inv_table;
void update(int x) {
if (MOD_NOW != mint::mod() || FACT_TABLE_SIZE == 0) {
fact_table.assign(1, 1);
fact_inv_table.assign(1, 1);
FACT_TABLE_SIZE = 1;
MOD_NOW = mint::mod();
}
while (FACT_TABLE_SIZE <= x) {
fact_table.resize(FACT_TABLE_SIZE * 2);
fact_inv_table.resize(FACT_TABLE_SIZE * 2);
for (int i = FACT_TABLE_SIZE; i < FACT_TABLE_SIZE * 2; ++i) {
fact_table[i] = fact_table[i - 1] * i;
}
fact_inv_table[FACT_TABLE_SIZE * 2 - 1] =
fact_table[FACT_TABLE_SIZE * 2 - 1].inv();
for (int i = FACT_TABLE_SIZE * 2 - 2; i >= FACT_TABLE_SIZE; --i) {
fact_inv_table[i] = fact_inv_table[i + 1] * (i + 1);
}
FACT_TABLE_SIZE *= 2;
}
}
inline mint fact(int x) {
assert(x >= 0);
update(x);
return fact_table[x];
}
inline mint fact_inv(int x) {
assert(x >= 0);
update(x);
return fact_inv_table[x];
}
inline mint comb(int x, int y) {
if (x < 0 || x < y || y < 0)
return 0;
return fact(x) * fact_inv(y) * fact_inv(x - y);
}
inline mint perm(int x, int y) { return fact(x) * fact_inv(x - y); }
// x個のグループにy個のものを分ける場合の数
inline mint multi_comb(int x, int y) {
if (y == 0 && x >= 0)
return 1;
if (y < 0 || x <= 0)
return 0;
return comb(x + y - 1, y);
}
#line 2 "cpplib/util/template.hpp"
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
using namespace std;
#line 1 "cpplib/util/ioutil.hpp"
// template <class Head,class... Args>
// std::ostream& output(std::ostream& out,const Head& head,const Args&... args){
// out>>head;
// return output(head,args...);
// }
// template <class Head>
// std::ostream& output(std::ostream& out,const Head& head){
// out>>head;
// return out;
// }
template <typename T, typename E>
std::ostream &operator<<(std::ostream &out, std::pair<T, E> v) {
out << "(" << v.first << "," << v.second << ")";
return out;
}
// template <class... Args>
// ostream& operator<<(ostream& out,std::tuple<Args...>v){
// std::apply(output,v);
// return out;
// }
#line 11 "cpplib/util/template.hpp"
struct __INIT__ {
__INIT__() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} __INIT__;
typedef long long lint;
constexpr long long INF = 1LL << 60;
constexpr int IINF = 1 << 30;
constexpr double EPS = 1e-10;
#ifndef REACTIVE
#define endl '\n';
#endif
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template <typename T> using V = vector<T>;
template <typename T> using VV = V<V<T>>;
#define output(t) \
{ \
bool f = 0; \
for (auto val : (t)) { \
cout << (f ? " " : "") << val; \
f = 1; \
} \
cout << endl; \
}
#define output2(t) \
{ \
for (auto i : t) \
output(i); \
}
#define debug(t) \
{ \
bool f = 0; \
for (auto i : t) { \
cerr << (f ? " " : "") << i; \
f = 1; \
} \
cerr << endl; \
}
#define debug2(t) \
{ \
for (auto i : t) \
debug(i); \
}
#define loop(n) for (long long _ = 0; _ < (long long)(n); ++_)
#define _overload4(_1, _2, _3, _4, name, ...) name
#define __rep(i, a) repi(i, 0, a, 1)
#define _rep(i, a, b) repi(i, a, b, 1)
#define repi(i, a, b, c) \
for (long long i = (long long)(a); i < (long long)(b); i += c)
#define rep(...) _overload4(__VA_ARGS__, repi, _rep, __rep)(__VA_ARGS__)
#define _overload3_rev(_1, _2, _3, name, ...) name
#define _rep_rev(i, a) repi_rev(i, 0, a)
#define repi_rev(i, a, b) \
for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define rrep(...) _overload3_rev(__VA_ARGS__, repi_rev, _rep_rev)(__VA_ARGS__)
#define all(n) begin(n), end(n)
template <typename T, typename E> bool chmin(T &s, const E &t) {
bool res = s > t;
s = min<T>(s, t);
return res;
}
template <typename T, typename E> bool chmax(T &s, const E &t) {
bool res = s < t;
s = max<T>(s, t);
return res;
}
const vector<lint> dx = {1, 0, -1, 0, 1, 1, -1, -1};
const vector<lint> dy = {0, 1, 0, -1, 1, -1, 1, -1};
#define SUM(v) accumulate(all(v), 0LL)
#if __cplusplus >= 201703L
template <typename T, typename... Args>
auto make_vector(T x, int arg, Args... args) {
if constexpr (sizeof...(args) == 0)
return vector<T>(arg, x);
else
return vector(arg, make_vector<T>(x, args...));
}
#endif
#define bit(n, a) ((n >> a) & 1)
#define extrep(v, ...) for (auto v : make_mat_impl({__VA_ARGS__}))
vector<vector<long long>> make_mat_impl(vector<long long> v) {
if (v.empty())
return vector<vector<long long>>(1, vector<long long>());
long long n = v.back();
v.pop_back();
vector<vector<long long>> ret;
vector<vector<long long>> tmp = make_mat_impl(v);
for (auto e : tmp)
for (long long i = 0; i < n; ++i) {
ret.push_back(e);
ret.back().push_back(i);
}
return ret;
}
using graph = vector<vector<int>>;
template <typename T> using graph_w = vector<vector<pair<int, T>>>;
#if __cplusplus >= 201703L
constexpr inline long long powll(long long a, long long b) {
long long res = 1;
while (b--)
res *= a;
return res;
}
#endif
template <typename T, typename E>
pair<T, E> &operator+=(pair<T, E> &s, const pair<T, E> &t) {
s.first += t.first;
s.second += t.second;
return s;
}
template <typename T, typename E>
pair<T, E> &operator-=(pair<T, E> &s, const pair<T, E> &t) {
s.first -= t.first;
s.second -= t.second;
return s;
}
template <typename T, typename E>
pair<T, E> operator+(const pair<T, E> &s, const pair<T, E> &t) {
auto res = s;
return res += t;
}
template <typename T, typename E>
pair<T, E> operator-(const pair<T, E> &s, const pair<T, E> &t) {
auto res = s;
return res -= t;
}
#define BEGIN_STACK_EXTEND(size) \
void *stack_extend_memory_ = malloc(size); \
void *stack_extend_origin_memory_; \
char *stack_extend_dummy_memory_ = (char *)alloca( \
(1 + (int)(((long long)stack_extend_memory_) & 127)) * 16); \
*stack_extend_dummy_memory_ = 0; \
asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp" \
: "=b"(stack_extend_origin_memory_) \
: "a"((char *)stack_extend_memory_ + (size)-1024));
#define END_STACK_EXTEND \
asm volatile("mov %%rax, %%rsp" ::"a"(stack_extend_origin_memory_)); \
free(stack_extend_memory_);
int floor_pow(int n) { return n ? 31 - __builtin_clz(n) : 0; }
#line 3 "main.cpp"
struct tree {
vector<lint> b;
vector<pair<lint, lint>> v;
lint n;
vec l, r;
vector<vector<tuple<lint, lint, lint>>> hist;
tree(vector<lint> &b) : b(b) {
n = b.size();
v.resize(b.size() * 4, make_pair(0, INF));
l.resize(b.size() * 4);
r.resize(b.size() * 4);
rep(i, n * 2) {
l[i + n * 2] = i;
r[i + n * 2] = i;
}
rrep(i, 1, n * 2) {
l[i] = l[i * 2];
r[i] = r[i * 2 + 1];
}
}
lint get(lint p, lint x, lint k) {
if (k - p < 0) {
return b[0] + (1LL << 40) * (p - k) + x;
}
if (k - p >= n) {
return b.back() + (1LL << 40) * (k - p - n + 1) + x;
}
return b[k - p] + x;
}
void add(lint p, lint x) {
lint now = 1;
hist.emplace_back();
while (1) {
lint mid = (l[now] + r[now]) / 2;
if (get(v[now].first, v[now].second, mid) > get(p, x, mid)) {
lint s = v[now].first;
lint t = v[now].second;
hist.back().emplace_back(now, s, t);
v[now] = make_pair(p, x);
p = s;
x = t;
}
// cerr << now << " " << n << endl;
if (now >= n * 2) {
break;
}
if (get(v[now].first, v[now].second, l[now]) > get(p, x, l[now])) {
now = now * 2;
} else if (get(v[now].first, v[now].second, r[now]) >
get(p, x, r[now])) {
now = now * 2 + 1;
} else {
break;
}
}
}
lint query(lint k) {
lint now = 1;
lint res = INF;
while (1) {
chmin(res, get(v[now].first, v[now].second, k));
if (now >= n * 2)
break;
if (l[now * 2] <= k && k <= r[now * 2]) {
now = now * 2;
} else {
now = now * 2 + 1;
}
}
return res;
}
void rollback() {
while (hist.back().size()) {
auto [now, s, t] = hist.back().back();
hist.back().pop_back();
v[now] = make_pair(s, t);
}
hist.pop_back();
}
};
void solve() {
lint n, q;
cin >> n >> q;
vector<lint> a(n);
vector<lint> b(n);
rep(i, n) cin >> a[i];
rep(i, n) cin >> b[i];
lint cnt = 1;
while (n & (n - 1)) {
++n;
a.emplace_back(INF);
b.emplace_back((1LL << 40) * cnt);
++cnt;
}
tree t(b);
lint sz = q;
while (sz & (sz - 1))
sz++;
vector<vector<pair<lint, lint>>> v(sz * 2);
// rep(i, n) {
// t.add(i, a[i]);
// }
vector<lint> qk(q);
vector<vector<pair<lint, lint>>> idx(n);
rep(i, q) {
lint p, x, k;
cin >> p >> x >> k;
--p;
k -= 2;
qk[i] = k;
if (i == 0) {
a[p] = x;
rep(j, n) { idx[j].emplace_back(0, a[j]); }
continue;
} else {
idx[p].emplace_back(i, x);
}
}
rep(i, n) { idx[i].emplace_back(q, -1); }
// debug2(idx);
rep(i, n) {
if (a[i] == INF)
continue;
rep(j, idx[i].size() - 1) {
lint l = idx[i][j].first;
lint r = idx[i][j + 1].first;
lint x = idx[i][j].second;
lint now = 1, s = 0, t = sz;
auto dfs = [&](auto dfs, lint now, lint s, lint t) {
if (l <= s && t <= r) {
v[now].emplace_back(i, x);
return;
}
lint mid = (s + t) / 2;
// [s,mid) と [l,r) が交差している
if (l < mid && s < r) {
dfs(dfs, now * 2, s, mid);
}
if (l < t && mid < r) {
dfs(dfs, now * 2 + 1, mid, t);
}
};
dfs(dfs, now, s, t);
}
}
auto dfs = [&](auto dfs, lint now) -> void {
for (auto [i, x] : v[now]) {
t.add(i, x);
}
if (now >= sz) {
if (now - sz < qk.size()) {
cout << t.query(qk[now - sz]) << endl;
}
}
if (now < sz) {
dfs(dfs, now * 2);
dfs(dfs, now * 2 + 1);
}
rep(i, v[now].size()) { t.rollback(); }
};
// cerr << t.hist.size() << endl;
dfs(dfs, 1);
// cerr << t.hist.size() << endl;
}
int main() {
solve();
// lint t;cin>>t;while(t--)solve();
}