結果
| 問題 | No.3516 Very Large Range Mod |
| コンテスト | |
| ユーザー |
 aPNJ777
|
| 提出日時 | 2026-04-24 21:47:57 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 974 ms / 2,000 ms |
| コード長 | 12,650 bytes |
| 記録 | |
| コンパイル時間 | 4,190 ms |
| コンパイル使用メモリ | 359,596 KB |
| 実行使用メモリ | 6,656 KB |
| 最終ジャッジ日時 | 2026-04-24 21:48:35 |
| 合計ジャッジ時間 | 24,615 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge4_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 30 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, w) vector<vector<type>> name(h, vector<type>(w))
#define vvv(type, name, h, w, l) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(l)))
#define vvvv(type, name, a, b, c, d) vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(d))))
#define vvvvv(type, name, a, b, c, d, e) vector<vector<vector<vector<vector<type>>>>> name(a, vector<vector<vector<vector<type>>>>(b, vector<vector<vector<type>>>(c, vector<vector<type>>(d, vector<type>(e)))))
#define elif else if
#define FOR1(a) for (long long _ = 0; _ < (long long)(a); _++)
#define FOR2(i, n) for (long long i = 0; i < (long long)(n); i++)
#define FOR3(i, l, r) for (long long i = l; i < (long long)(r); i++)
#define FOR4(i, l, r, c) for (long long i = l; i < (long long)(r); i += c)
#define FOR1_R(a) for (long long _ = (long long)(a) - 1; _ >= 0; _--)
#define FOR2_R(i, n) for (long long i = (long long)(n) - 1; i >= (long long)(0); i--)
#define FOR3_R(i, l, r) for (long long i = (long long)(r) - 1; i >= (long long)(l); i--)
#define FOR4_R(i, l, r, c) for (long long i = (long long)(r) - 1; i >= (long long)(l); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_in(a, A) for (auto a: A)
#define FOR_each(a, A) for (auto &&a: A)
#define FOR_subset(t, s) for(long long t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) int(x.size())
int popcount(int x) { return __builtin_popcount(x); }
int popcount(uint32_t x) { return __builtin_popcount(x); }
int popcount(long long x) { return __builtin_popcountll(x); }
int popcount(uint64_t x) { return __builtin_popcountll(x); }
// __builtin_clz(x)は最上位bitからいくつ0があるか.
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(uint32_t x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(long long x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(uint64_t x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// 入力
void rd() {}
void rd(char &c) { cin >> c; }
void rd(string &s) { cin >> s; }
void rd(int &x) { cin >> x; }
void rd(uint32_t &x) { cin >> x; }
void rd(long long &x) { cin >> x; }
void rd(uint64_t &x) { cin >> x; }
template<class T>
void rd(vector<T> &v) {
for (auto& x:v) rd(x);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define STRING(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
uint32_t __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
uint64_t __VA_ARGS__; \
read(__VA_ARGS__)
#define VC(t, a, n) \
vector<t> a(n); \
read(a)
#define VVC(t, a, h, w) \
vector<vector<t>> a(h, vector<t>(w)); \
read(a)
//出力
void wt() {}
void wt(const char c) { cout << c; }
void wt(const string s) { cout << s; }
void wt(int x) { cout << x; }
void wt(uint32_t x) { cout << x; }
void wt(long long x) { cout << x; }
void wt(uint64_t x) { cout << x; }
void wt(double x) { cout << fixed << setprecision(16) << x; }
void wt(long double x) { cout << fixed << setprecision(16) << x; }
template<class T>
void wt(const vector<T> v) {
int n = v.size();
for (int i = 0; i < n; i++) {
if (i) wt(' ');
wt(v[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
/////////////////////////////////////////////////////////////////////////////////////////
template <class T>
int bisect_left(const vector<T> &A, T x) {
auto idx = lower_bound(A.begin(), A.end(), x) - A.begin();
return idx;
}
template <class T>
int bisect_right(const vector<T> &A, T x) {
auto idx = upper_bound(A.begin(), A.end(), x) - A.begin();
return idx;
}
long long min(long long a, long long b) { return a < b ? a : b; }
template <class T>
T min(vector<T> A) {
assert (A.size());
T S = A[0];
for (T a : A) S = min(a, S);
return S;
}
long long max(long long a, long long b) { return a > b ? a : b; }
template <class T>
T max(vector<T> A) {
assert (A.size());
T S = A[0];
for (T a : A) S = max(a, S);
return S;
}
long long add(long long x, long long y) { return x + y; }
template <class mint>
mint add(mint x, mint y) { return x + y; }
template <class T>
bool chmin(T & x, T a) { return a < x ? (x = a, true) : false; }
template <class T>
bool chmax(T & x, T a) { return a > x ? (x = a, true) : false; }
template <class T>
T sum(vector<T> A) {
T S = 0;
for (int i = 0; i < int(A.size()); i++) S += A[i];
return S;
}
uint64_t random_u64(uint64_t l, uint64_t r) {
static std::random_device rd;
static std::mt19937_64 gen(rd());
std::uniform_int_distribution<uint64_t> dist(l, r);
return dist(gen);
}
long long gcd(long long a, long long b) {
while (a) {
b %= a;
if (b == 0) return a;
a %= b;
}
return b;
}
long long lcm(long long a, long long b) {
if (a * b == 0) return 0;
return a * b / gcd(a, b);
}
long long pow_mod(long long a, long long r, long long mod) {
long long res = 1, p = a % mod;
while (r) {
if ((r % 2) == 1) res = res * p % mod;
p = p * p % mod, r >>= 1;
}
return res;
}
long long mod_inv(long long a, long long mod) {
if (mod == 1) return 0;
a %= mod;
long long b = mod, s = 1, t = 0;
while (1) {
if (a == 1) return s;
t -= (b / a) * s;
b %= a;
if (b == 1) return t + mod;
s -= (a / b) * t;
a %= b;
}
}
long long Garner(vector<long long> Rem, vector<long long> Mod, int MOD) {
assert (Rem.size() == Mod.size());
long long mod = MOD;
Rem.push_back(0);
Mod.push_back(mod);
long long n = Mod.size();
vector<long long> coffs(n, 1);
vector<long long> constants(n, 0);
for (int i = 0; i < n - 1; i++) {
long long v = (Mod[i] + Rem[i] - constants[i]) % Mod[i];
v *= mod_inv(coffs[i], Mod[i]);
v %= Mod[i];
for (int j = i + 1; j < n; j++) {
constants[j] = (constants[j] + coffs[j] * v) % Mod[j];
coffs[j] = (coffs[j] * Mod[i]) % Mod[j];
}
}
return constants[n - 1];
}
long long Tonelli_Shanks(long long a, long long mod) {
a %= mod;
if (a < 2) return a;
if (pow_mod(a, (mod - 1) / 2, mod) != 1) return -1;
if (mod % 4 == 3) return pow_mod(a, (mod + 1) / 4, mod);
long long b = 3;
if (mod != 998244353) {
while (pow_mod(b, (mod - 1) / 2, mod) == 1) {
b = random_u64(2, mod - 1);
}
}
long long q = mod - 1;
long long Q = 0;
while (q % 2 == 0) {
Q++, q /= 2;
}
long long x = pow_mod(a, (q + 1) / 2, mod);
b = pow_mod(b, q, mod);
long long shift = 2;
while ((x * x) % mod != a) {
long long error = (((pow_mod(a, mod - 2, mod) * x) % mod) * x) % mod;
if (pow_mod(error, 1 << (Q - shift), mod) != 1) {
x = (x * b) % mod;
}
b = (b * b) % mod;
shift++;
}
return x;
}
long long floor_div(long long a, long long b) {
if (b < 0) a *= -1, b *= -1;
if (a >= 0) return a / b;
return -((-a + b - 1) / b);
}
long long ceil_div(long long a, long long b) {
if (b < 0) a *= -1, b *= -1;
if (a >= 0) return (a + b - 1) / b;
return - ((-a) / b);
}
/////////////////////////////////////////////////////////////////////////////////////////
/*
検索するとき
https://www.google.com/search?udm=14&q=
-ai
*/
// https://atcoder.jp/contests/arc183/editorial/10768
template <typename Monoid, typename T>
T monoid_prod_on_floorpath(T x, T y, uint64_t N, uint64_t M, uint64_t A, uint64_t B) {
uint64_t C = (A * N + B) / M;
T pre = Monoid::e(), suf = Monoid::e();
while (1) {
uint64_t p = A / M, q = B / M;
A %= M, B %= M;
x = Monoid::op(x, Monoid::pow(y, p));
pre = Monoid::op(pre, Monoid::pow(y, q));
C -= (p * N + q);
if (C == 0) break;
uint64_t D = (M * C - B - 1) / A + 1;
suf = Monoid::op(y, Monoid::op(Monoid::pow(x, N - D), suf));
B = M - B + A - 1, N = C - 1, C = D;
swap(M, A), swap(x, y);
}
x = Monoid::pow(x, N);
return Monoid::op(Monoid::op(pre, x), suf);
}
template <typename T, int K, int L>
struct Monoid_floor_sum {
static const int N = max(K, L);
struct data {
array<array<T, L + 1>, K + 1> table;
T x, y;
};
static data e() {
T x = T(0), y = T(0);
return {array<array<T, L + 1>, K + 1> {}, x, y};
}
static data op(data a, data b) {
static T binom[N + 1][N + 1];
if (binom[0][0] != T(1)) {
binom[0][0] = T(1);
for (int i = 0; i < N; i++) {
for (int j = 0; j <= i; j++) binom[i + 1][j] += binom[i][j], binom[i + 1][j + 1] += binom[i][j];
}
}
array<T, K + 1> X;
array<T, L + 1> Y;
X[0] = T(1), Y[0] = T(1);
for (int i = 0; i < K; i++) X[i + 1] = X[i] * a.x;
for (int i = 0; i < L; i++) Y[i + 1] = Y[i] * a.y;
// b の x^iy^j を x^i(y + a.y)^j にする
for (int i = 0; i <= K; i++) {
for (int j = L; j >= 0; j--) {
T p = b.table[i][j];
for (int k = j + 1; k <= L; k++) b.table[i][k] += binom[k][j] * Y[k - j] * p;
}
}
// b の x^i(y + a.y)^j を (x + a.x)^i(y + a.y)^j にしたものを a に足す.
for (int j = 0; j <= L; j++) {
for (int i = K; i >= 0; i--) {
for (int k = i; k <= K; k++) a.table[k][j] += binom[k][i] * X[k - i] * b.table[i][j];
}
}
a.x += b.x, a.y += b.y;
return a;
}
static data pow(data a, long long k) {
data res = e(), p = a;
while (k) {
if (k & 1) res = op(res, p);
p = op(p, p), k >>= 1;
}
return res;
}
static data X() {
data x = e();
x.table[0][0] = T(1), x.x = T(1);
return x;
}
static data Y() {
data y = e();
y.y = T(1);
return y;
}
};
template <typename mint, typename mono>
mint calc_floor_sum(long long N, long long M, long long A, long long B, long long p, long long q) {
if (M < 0) A *= -1, B *= -1, M *= -1;
mint neg = 1;
if (A < 0) neg = mint(-1), B = M - 1 - B, A *= -1;
long long b = B / M;
B %= M;
if (B < 0) b -= 1, B += M;
using T = typename mono::data;
T x = mono::X(), y = mono::Y();
T res = monoid_prod_on_floorpath<mono, T>(x, y, N, M, A, B);
T offset = mono::e();
offset.y = mint(b);
res = mono::op(offset, res);
mint ans = res.table[p][q];
if (q % 2) ans *= neg;
return ans;
}
template <typename mint>
mint floor_sum(long long N, long long M, long long A, long long B, long long p, long long q) {
if (p == 0 && q == 1) return calc_floor_sum<mint, Monoid_floor_sum<mint, 0, 1>>(N, M, A, B, p, q);
if (max(p, q) <= 1) return calc_floor_sum<mint, Monoid_floor_sum<mint, 1, 1>>(N, M, A, B, p, q);
else if (max(p, q) <= 2) return calc_floor_sum<mint, Monoid_floor_sum<mint, 2, 2>>(N, M, A, B, p, q);
else if (max(p, q) <= 4) return calc_floor_sum<mint, Monoid_floor_sum<mint, 4, 4>>(N, M, A, B, p, q);
else if (max(p, q) <= 7) return calc_floor_sum<mint, Monoid_floor_sum<mint, 7, 7>>(N, M, A, B, p, q);
else return calc_floor_sum<mint, Monoid_floor_sum<mint, 10, 10>>(N, M, A, B, p, q);
}
void solve() {
LL(N, K, M);
VC(ll, B, N);
VC(ll, C, N);
int i = 0;
ll b = B[0], c = C[0];
ll R = 0;
while (K) {
ll d = min(b, K);
K -= d, b -= d;
R += c * d % M;
if (R >= M) R -= M;
if (b == 0) b = B[++i], c = C[i];
}
int j = 0;
ll bb = B[0], cc = C[0];
ll ans = 0;
if (R == 0) ans++;
while (i < N) {
ll d = min(b, bb);
ll e = (c - cc) % M;
if (e < 0) e += M;
ans += floor_sum<long long>(d, M, e, R + e + M, 0, 1) - floor_sum<long long>(d, M, e, R + e + M - 1, 0, 1);
b -= d, bb -= d;
R += e * d % M;
if (R >= M) R -= M;
if (b == 0) {
i++;
if (i == N) break;
b = B[i], c = C[i];
}
if (bb == 0) bb = B[++j], cc = C[j];
}
print(ans);
}
int main() {
//ios::sync_with_stdio(false);
//cin.tie(nullptr);
int T = 1;
//cin >> T;
FOR(T) solve();
}