QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#394759#7782. Ursa MinorwsyearTL 1691ms151948kbC++175.5kb2024-04-20 19:15:292024-04-20 19:15:30

Judging History

你现在查看的是最新测评结果

  • [2024-04-20 19:15:30]
  • 评测
  • 测评结果:TL
  • 用时:1691ms
  • 内存:151948kb
  • [2024-04-20 19:15:29]
  • 提交

answer

// Author: Klay Thompson
// Problem: # 7782. Ursa Minor
// Memory Limit: 1024 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T>inline void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T>inline void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

template <int P>
class mod_int {
  using Z = mod_int;

private:
  static int mo(int x) { return x < 0 ? x + P : x; }

public:
  int x;
  int val() const { return x; }
  mod_int() : x(0) {}
  template <class T>
  mod_int(const T &x_) : x(x_ >= 0 && x_ < P ? static_cast<int>(x_) : mo(static_cast<int>(x_ % P))) {}
  bool operator==(const Z &rhs) const { return x == rhs.x; }
  bool operator!=(const Z &rhs) const { return x != rhs.x; }
  Z operator-() const { return Z(x ? P - x : 0); }
  Z pow(long long k) const {
    Z res = 1, t = *this;
    while (k) {
      if (k & 1) res *= t;
      if (k >>= 1) t *= t;
    }
    return res;
  }
  Z &operator++() {
    x < P - 1 ? ++x : x = 0;
    return *this;
  }
  Z &operator--() {
    x ? --x : x = P - 1;
    return *this;
  }
  Z operator++(int) {
    Z ret = x;
    x < P - 1 ? ++x : x = 0;
    return ret;
  }
  Z operator--(int) {
    Z ret = x;
    x ? --x : x = P - 1;
    return ret;
  }
  Z inv() const { return pow(P - 2); }
  Z &operator+=(const Z &rhs) {
    (x += rhs.x) >= P && (x -= P);
    return *this;
  }
  Z &operator-=(const Z &rhs) {
    (x -= rhs.x) < 0 && (x += P);
    return *this;
  }
  Z &operator*=(const Z &rhs) {
    x = 1ULL * x * rhs.x % P;
    return *this;
  }
  Z &operator/=(const Z &rhs) { return *this *= rhs.inv(); }
#define setO(T, o)                                 \
  friend T operator o(const Z &lhs, const Z &rhs) {\
    Z res = lhs;                                   \
    return res o## = rhs;                          \
  }
  setO(Z, +) setO(Z, -) setO(Z, *) setO(Z, /)
#undef setO
};
const int P = 1011451423;
using Z = mod_int<P>;

const int maxn = 200010;
const int maxm = 100;
const int B = 80;
const Z iv2 = Z(2).inv();
const Z iv6 = Z(6).inv();

int n, m, q, d[maxn], st[maxn][20];
ll a[maxn], pool[maxn * maxm], *used = pool;

struct fwt {
  int n;
  ll *t;
  fwt() { }
  fwt(int m) { n = m, t = used, used += m + 3; }
  void upd(int x, ll v) {
    while (x <= n) t[x] += v, x += x & (-x);
  }
  ll qry(int x) {
    ll res = 0;
    while (x) res += t[x], x -= x & (-x);
    return res;
  }
} t[maxm][maxm];

struct FWT {
  Z t[maxn];
  void upd(int x, Z v) {
    x++;
    while (x <= n) t[x] += v, x += x & (-x);
  }
  Z qry(int x) {
    x++;
    Z res = 0;
    while (x) res += t[x], x -= x & (-x);
    return res;
  }
} t0, t1, t2;

Z sum(int n) {
  return Z(n) * (n + 1) * iv2;
}

Z sum2(int n) {
  return Z(n) * (n + 1) * (2 * n + 1) * iv6;
}

int que(int l, int r) {
  int k = __lg(r - l + 1);
  return gcd(st[l][k], st[r - (1 << k) + 1][k]);
}

int main() {
  cin.tie(nullptr) -> ios::sync_with_stdio(false);
  cin >> n >> m >> q;
  rep (i, 0, n - 1) cin >> a[i];
  rep (i, 1, m) cin >> st[i][0];
  rep (j, 1, 19) rep (i, 1, m - (1 << j) + 1)
    st[i][j] = gcd(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
  rep (i, 1, B) rep (j, 0, i - 1) t[i][j] = fwt(n / i + 5);
  rep (i, 0, n - 1) rep (j, 1, B) t[j][i % j].upd(i / j + 1, a[i]);
  rep (i, 0, n - 1) t0.upd(i, Z(a[i])), t1.upd(i, Z(i) * a[i]), t2.upd(i, Z(i) * i * a[i]);
  while (q--) {
    string op;
    cin >> op;
    if (op == "U") {
      int x;
      cin >> x, x--;
      rep (i, 1, B) t[i][x % i].upd(x / i + 1, -a[x]);
      t0.upd(x, -Z(a[x])), t1.upd(x, -Z(x) * a[x]), t2.upd(x, -Z(x) * x * a[x]);
      cin >> a[x];
      rep (i, 1, B) t[i][x % i].upd(x / i + 1, a[x]);
      t0.upd(x, Z(a[x])), t1.upd(x, Z(x) * a[x]), t2.upd(x, Z(x) * x * a[x]);
    } else {
      int l, r, S, T, ok = 1;
      cin >> l >> r >> S >> T, l--, r--;
      int g = gcd(r - l + 1, que(S, T));
      ll lst = 0;
      if (g <= B) {
        ll lst = 0;
        bool ok = 1;
        rep (i, 0, g - 1) {
          ll L = l + i, R = r - g + i + 1, rg = L % g;
          ll sum = t[g][rg].qry(R / g + 1) - t[g][rg].qry(L / g);
          if (i && sum != lst) { ok = 0; break; }
          lst = sum;
        }
        cout << (ok ? "Yes" : "No") << '\n';
      } else if (r - l + 1 <= 50) {
        rep (i, 0, g - 1) {
          ll sum = 0;
          for (int j = l + i; j <= r; j += g) sum += a[j];
          if (i) ok &= (sum == lst);
          if (!ok) break;
          lst = sum;
        }
        cout << (ok ? "Yes" : "No") << '\n';
      } else {
        Z ss0 = 0, ss1 = 0, ss2 = 0;
        for (int pl = l, pr = l + g - 1; pr <= r; pl += g, pr += g) {
          Z s0 = t0.qry(pr) - t0.qry(pl), s1 = t1.qry(pr) - t1.qry(pl), s2 = t2.qry(pr) - t2.qry(pl);
          Z rs0 = s0, rs1 = s1 - s0 * pl, rs2 = s2 - rs1 * pl * 2 - s0 * pl * pl;
          rs0 -= Z(a[pl]) * (g - 1), rs1 -= Z(a[pl]) * sum(g - 1), rs2 -= Z(a[pl]) * sum2(g - 1);
          ss0 += rs0, ss1 += rs1, ss2 += rs2;
        }
        cerr << ss0.val() << ' ' << ss1.val() << ' ' << ss2.val() << '\n';
        if ((ss0.val() || ss1.val() || ss2.val())) cout << "No\n";
        else cout << "Yes\n";
      }
    }
  }
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 8700kb

input:

6 4 5
1 1 4 5 1 4
3 3 2 4
Q 1 5 1 2
Q 2 5 3 4
U 5 2
Q 1 6 1 2
Q 2 5 3 4

output:

Yes
No
No
Yes

result:

ok 4 tokens

Test #2:

score: 0
Accepted
time: 1ms
memory: 8772kb

input:

1 1 1
0
1
Q 1 1 1 1

output:

Yes

result:

ok "Yes"

Test #3:

score: 0
Accepted
time: 196ms
memory: 10716kb

input:

2000 2000 200000
1 1 2 0 0 2 0 2 0 0 0 0 0 2 2 1 2 0 0 2 2 2 1 0 1 2 1 2 0 0 1 1 1 2 0 0 2 2 2 2 0 2 0 0 2 1 2 0 0 1 2 2 1 0 2 0 0 0 1 2 2 1 2 2 0 0 1 1 1 0 0 2 0 0 1 1 0 2 2 2 1 0 0 1 0 1 2 2 2 1 1 2 2 1 2 1 0 2 2 3 1 3 2 3 1 0 1 2 0 1 1 1 0 2 2 3 2 0 3 2 3 3 1 2 3 1 2 0 1 0 3 1 0 0 2 0 1 2 1 3 2 2...

output:

Yes
Yes
No
Yes
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
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No
Yes
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Yes
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Yes
No
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No
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No...

result:

ok 100554 tokens

Test #4:

score: 0
Accepted
time: 111ms
memory: 23892kb

input:

1 200000 200000
998244353
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

output:

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
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Yes
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Yes
Yes
Yes
Yes
Yes
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Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
...

result:

ok 100240 tokens

Test #5:

score: 0
Accepted
time: 103ms
memory: 18704kb

input:

6 131072 200000
0 0 0 0 1000000000 1000000000
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ...

output:

Yes
Yes
Yes
No
No
No
Yes
No
No
No
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
No
No
No
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Yes
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Yes
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Yes
No
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Yes
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No
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No
No
No
Yes
No
No
No
No
No
No
Yes
Yes
No
Yes
N...

result:

ok 100021 tokens

Test #6:

score: 0
Accepted
time: 1403ms
memory: 151948kb

input:

200000 200000 200000
490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877 490339877...

output:

No
No
No
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
No
Yes
No
No
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Yes
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No
No
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Yes
No
Yes
Yes
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No
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No
No
No
No
No
N...

result:

ok 187340 tokens

Test #7:

score: 0
Accepted
time: 1541ms
memory: 151164kb

input:

200000 200000 200000
360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531 360543531...

output:

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
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Yes
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Yes
Yes
Yes
Yes
Yes
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Yes
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Yes
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Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
...

result:

ok 199985 tokens

Test #8:

score: 0
Accepted
time: 1691ms
memory: 151160kb

input:

200000 200000 200000
793134805 922104801 158394038 993313213 77527653 992889267 148461787 499165677 132176015 189185554 783374975 332147281 923925325 371040161 393285793 437388761 138662855 212488140 265392646 498903298 578518594 550390771 960084339 408548934 56106823 814997309 456913457 300689692 1...

output:

No
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
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No
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No
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No
No
Yes
No
No
No
No
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No
No
Yes
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No
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No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
Yes
No...

result:

ok 200000 tokens

Test #9:

score: 0
Accepted
time: 1616ms
memory: 151232kb

input:

200000 200000 200000
451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037 451942036 451942035 451942037...

output:

No
No
No
No
Yes
No
Yes
No
No
No
No
Yes
No
No
No
Yes
No
Yes
No
No
No
No
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No
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No
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Yes
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No
No
No
No
Yes
No
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Yes
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Yes
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Yes
No
Yes
No
No
No
No
Yes
No
No
Yes
No
No
No
No
No
No
No
No
Yes
No
Yes
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No
No
Yes
No
Yes
No
No
Yes
No
Yes
No
No
No
Yes
No
No
No
No
No
No
No
No
N...

result:

ok 199977 tokens

Test #10:

score: 0
Accepted
time: 1254ms
memory: 150924kb

input:

200000 200000 200000
606894463 710609424 913364361 30426550 801940265 516097169 349718376 606894463 710609424 913364361 30426550 801940265 516097169 349718376 606894463 710609424 913364361 30426550 801940265 516097169 349718376 606894463 710609424 913364361 30426550 801940265 516097169 349718376 606...

output:

No
No
No
Yes
No
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
Yes
No
No
No
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No
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Yes
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No
Yes
No
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No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
No
Yes
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
N...

result:

ok 100329 tokens

Test #11:

score: -100
Time Limit Exceeded

input:

200000 199999 200000
903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886 903745886...

output:

Yes
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
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No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No
No...

result: