結果

問題 No.856 増える演算
ユーザー 👑 hos.lyrichos.lyric
提出日時 2019-07-26 22:50:33
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 526 ms / 3,153 ms
コード長 9,447 bytes
コンパイル時間 1,540 ms
コンパイル使用メモリ 159,356 KB
実行使用メモリ 32,736 KB
最終ジャッジ日時 2024-06-22 02:07:25
合計ジャッジ時間 32,196 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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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 192 ms
26,440 KB
testcase_01 AC 157 ms
26,640 KB
testcase_02 AC 172 ms
26,656 KB
testcase_03 AC 203 ms
26,984 KB
testcase_04 AC 222 ms
28,444 KB
testcase_05 AC 214 ms
28,176 KB
testcase_06 AC 206 ms
26,848 KB
testcase_07 AC 215 ms
27,760 KB
testcase_08 AC 211 ms
27,696 KB
testcase_09 AC 183 ms
26,860 KB
testcase_10 AC 208 ms
26,816 KB
testcase_11 AC 226 ms
28,528 KB
testcase_12 AC 209 ms
27,720 KB
testcase_13 AC 305 ms
28,388 KB
testcase_14 AC 291 ms
26,772 KB
testcase_15 AC 297 ms
28,904 KB
testcase_16 AC 292 ms
26,236 KB
testcase_17 AC 294 ms
26,804 KB
testcase_18 AC 272 ms
26,364 KB
testcase_19 AC 278 ms
28,376 KB
testcase_20 AC 281 ms
27,380 KB
testcase_21 AC 280 ms
26,728 KB
testcase_22 AC 291 ms
27,920 KB
testcase_23 AC 213 ms
24,632 KB
testcase_24 AC 218 ms
24,840 KB
testcase_25 AC 221 ms
24,440 KB
testcase_26 AC 218 ms
24,016 KB
testcase_27 AC 212 ms
23,140 KB
testcase_28 AC 215 ms
24,200 KB
testcase_29 AC 216 ms
24,492 KB
testcase_30 AC 218 ms
24,196 KB
testcase_31 AC 218 ms
24,220 KB
testcase_32 AC 217 ms
25,272 KB
testcase_33 AC 338 ms
25,044 KB
testcase_34 AC 349 ms
25,164 KB
testcase_35 AC 340 ms
25,284 KB
testcase_36 AC 347 ms
24,696 KB
testcase_37 AC 341 ms
25,036 KB
testcase_38 AC 327 ms
25,140 KB
testcase_39 AC 337 ms
24,228 KB
testcase_40 AC 344 ms
24,508 KB
testcase_41 AC 335 ms
24,012 KB
testcase_42 AC 347 ms
25,272 KB
testcase_43 AC 338 ms
24,304 KB
testcase_44 AC 302 ms
23,516 KB
testcase_45 AC 338 ms
23,476 KB
testcase_46 AC 339 ms
24,024 KB
testcase_47 AC 334 ms
23,648 KB
testcase_48 AC 340 ms
25,460 KB
testcase_49 AC 331 ms
24,476 KB
testcase_50 AC 341 ms
25,460 KB
testcase_51 AC 349 ms
25,060 KB
testcase_52 AC 345 ms
24,716 KB
testcase_53 AC 486 ms
27,332 KB
testcase_54 AC 450 ms
25,352 KB
testcase_55 AC 479 ms
27,216 KB
testcase_56 AC 434 ms
24,336 KB
testcase_57 AC 476 ms
26,456 KB
testcase_58 AC 466 ms
26,564 KB
testcase_59 AC 492 ms
27,976 KB
testcase_60 AC 447 ms
25,244 KB
testcase_61 AC 490 ms
27,220 KB
testcase_62 AC 483 ms
27,588 KB
testcase_63 AC 378 ms
24,184 KB
testcase_64 AC 485 ms
26,548 KB
testcase_65 AC 436 ms
25,112 KB
testcase_66 AC 455 ms
25,908 KB
testcase_67 AC 455 ms
27,192 KB
testcase_68 AC 493 ms
27,252 KB
testcase_69 AC 483 ms
27,368 KB
testcase_70 AC 516 ms
27,772 KB
testcase_71 AC 479 ms
28,360 KB
testcase_72 AC 474 ms
26,412 KB
testcase_73 AC 494 ms
31,716 KB
testcase_74 AC 501 ms
31,548 KB
testcase_75 AC 502 ms
31,396 KB
testcase_76 AC 503 ms
31,912 KB
testcase_77 AC 509 ms
32,572 KB
testcase_78 AC 526 ms
32,712 KB
testcase_79 AC 506 ms
32,004 KB
testcase_80 AC 505 ms
32,048 KB
testcase_81 AC 497 ms
32,736 KB
testcase_82 AC 202 ms
31,812 KB
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コンパイルメッセージ
Main.d(332): Deprecation: function `std.math.exponential.log` is deprecated - `std.math.exponential.log` called with argument types `(long)` matches both `log(real)`, `log(double)`, and `log(float)`. Cast argument to floating point type instead.
Main.d(332): Deprecation: function `std.math.exponential.log` is deprecated - `std.math.exponential.log` called with argument types `(long)` matches both `log(real)`, `log(double)`, and `log(float)`. Cast argument to floating point type instead.

ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


struct ModInt(long M) {
  long x;
  this(in ModInt a) { x = a.x; }
  this(in long a) { x = a % M; if (x < 0) x += M; }
  ref ModInt opAssign(in long a) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op)(in ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x *= a.x; x %= M; }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(in long a) { return mixin("this " ~ op ~ "= ModInt(a)"); }
  ModInt opUnary(string op)() const if (op == "-") { return ModInt(-x); }
  ModInt opBinary(string op, T)(in T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op)(in long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  string toString() const { return x.to!string; }
}


// a^-1 (mod 2^64)
long modInv(long a)
in {
  assert(a & 1, "modInv: a must be odd");
}
do {
  long b = ((a << 1) + a) ^ 2;
  b *= 2 - a * b;
  b *= 2 - a * b;
  b *= 2 - a * b;
  b *= 2 - a * b;
  return b;
}

// a^-1 (mod m)
long modInv(long a, long m)
in {
  assert(m > 0, "modInv: m > 0 must hold");
}
do {
  long b = m, x = 1, y = 0, t;
  for (; ; ) {
    t = a / b;
    a -= t * b;
    if (a == 0) {
      assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
      if (b == -1) {
        y = -y;
      }
      return (y < 0) ? (y + m) : y;
    }
    x -= t * y;
    t = b / a;
    b -= t * a;
    if (b == 0) {
      assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
      if (a == -1) {
        x = -x;
      }
      return (x < 0) ? (x + m) : x;
    }
    y -= t * x;
  }
}

// 2^-31 a (mod M)
long montgomery(long M)(long a) if (1 <= M && M <= 0x7fffffff && (M & 1))
in {
  assert(0 <= a && a < (M << 31), "montgomery: 0 <= a < 2^31 M must hold");
}
do {
  enum negInvM = -modInv(M) & 0x7fffffff;
  const b = (a + ((a * negInvM) & 0x7fffffff) * M) >> 31;
  return (b >= M) ? (b - M) : b;
}

// FFT on Z / M Z with Montgomery multiplication (x -> 2^31 x)
//   G: primitive 2^K-th root of unity
class FFT(long M, int K, long G)
    if (is(typeof(montgomery!(M)(0))) && K >= 0 && 0 < G && G < M) {
  import std.algorithm : swap;
  import core.bitop : bsf;

  int n, invN;
  long[] g;

  this(int n)
  in {
    assert(!(n & (n - 1)), "FFT.this: n must be a power of 2");
    assert(4 <= n && n <= 1 << K, "FFT.this: 4 <= n <= 2^K must hold");
  }
  do {
    this.n = n;
    this.invN = ((1L << 31) / n) % M;
    g.length = n + 1;
    g[0] = (1L << 31) % M;
    g[1] = (G << 31) % M;
    foreach (_; 0 .. K - bsf(n)) {
      g[1] = montgomery!(M)(g[1] * g[1]);
    }
    foreach (i; 2 .. n + 1) {
      g[i] = montgomery!(M)(g[i - 1] * g[1]);
    }
    assert(g[0] != g[n >> 1] && g[0] == g[n],
           "FFT.this: G must be a primitive 2^K-th root of unity");
    for (int i = 0, j = 0; i < n >> 1; ++i) {
      if (i < j) {
        swap(g[i], g[j]);
        swap(g[n - i], g[n - j]);
      }
      for (int m = n >> 1; (m >>= 1) && !((j ^= m) & m); ) {}
    }
  }

  void fftMontgomery(long[] x, bool inv)
  in {
    assert(x.length == n, "FFT.fftMontgomery: |x| = n must hold");
  }
  do {
    foreach_reverse (h; 0 .. bsf(n)) {
      const l = 1 << h;
      foreach (i; 0 .. n >> 1 >> h) {
        const gI = g[inv ? (n - i) : i];
        foreach (j; i << 1 << h .. ((i << 1) + 1) << h) {
          const t = montgomery!(M)(gI * x[j + l]);
          if ((x[j + l] = x[j] - t) < 0) {
            x[j + l] += M;
          }
          if ((x[j] += t) >= M) {
            x[j] -= M;
          }
        }
      }
    }
    for (int i = 0, j = 0; i < n; ++i) {
      if (i < j) {
        swap(x[i], x[j]);
      }
      for (int m = n; (m >>= 1) && !((j ^= m) & m); ) {}
    }
    if (inv) {
      foreach (i; 0 .. n) {
        x[i] = montgomery!(M)(invN * x[i]);
      }
    }
  }

  long[] convolution(long[] a, long[] b)
  in {
    assert(a.length <= n, "FFT.convolution: |a| <= n must hold");
    assert(b.length <= n, "FFT.convolution: |b| <= n must hold");
  }
  do {
    auto x = new long[n], y = new long[n];
    foreach (i; 0 .. a.length) {
      const t = a[i] % M;
      x[i] = (((t < 0) ? (t + M) : t) << 31) % M;
    }
    foreach (i; 0 .. b.length) {
      const t = b[i] % M;
      y[i] = (((t < 0) ? (t + M) : t) << 31) % M;
    }
    fftMontgomery(x, false);
    fftMontgomery(y, false);
    foreach (i; 0 .. n) {
      x[i] = montgomery!(M)(x[i] * y[i]);
    }
    fftMontgomery(x, true);
    foreach (i; 0 .. n) {
      x[i] = montgomery!(M)(x[i]);
    }
    return x;
  }
}

// P0 P1 P2 > 2^90, P0 + P1 + P2 = 2^32 + 3
enum FFT_P0 = 2013265921L;  // 2^27 15 + 1
enum FFT_P1 = 1811939329L;  // 2^26 27 + 1
enum FFT_P2 =  469762049L;  // 2^26  7 + 1
alias FFT0 = FFT!(FFT_P0, 27, 440564289L);  // 31^15
alias FFT1 = FFT!(FFT_P1, 26,  72705542L);  // 13^27
alias FFT2 = FFT!(FFT_P2, 26,      2187L);  //  3^ 7

// Convolution of a and b (indices mod fft0.n)
//   modify a and b so that 0 <= a[i] < m, 0 <= b[i] < m
long[] convolution(FFT0 fft0, FFT1 fft1, FFT2 fft2, long[] a, long[] b, long m)
in {
  assert(fft0.n == fft1.n && fft0.n == fft2.n, "convolution: fft0.n = fft1.n = fft2.n must hold");
  assert(1 <= m && m <= 0x7fffffff, "convolution: 1 <= m < 2^31 must hold");
}
do {
  enum FFT_INV01 = modInv(FFT_P0, FFT_P1);
  enum FFT_INV012 = modInv(FFT_P0 * FFT_P1, FFT_P2);
  foreach (i; 0 .. a.length) {
    if ((a[i] %= m) < 0) {
      a[i] += m;
    }
  }
  foreach (i; 0 .. b.length) {
    if ((b[i] %= m) < 0) {
      b[i] += m;
    }
  }
  const x0 = fft0.convolution(a, b);
  const x1 = fft1.convolution(a, b);
  const x2 = fft2.convolution(a, b);
  auto x = new long[fft0.n];
  foreach (i; 0 .. fft0.n) {
    auto y0 = x0[i] % FFT_P0;
    auto y1 = (FFT_INV01 * (x1[i] - y0)) % FFT_P1;
    if (y1 < 0) {
      y1 += FFT_P1;
    }
    auto y2 = (FFT_INV012 * ((x2[i] - y0 - FFT_P0 * y1) % FFT_P2)) % FFT_P2;
    if (y2 < 0) {
      y2 += FFT_P2;
    }
    x[i] = (y0 + FFT_P0 * y1 + ((FFT_P0 * FFT_P1) % m) * y2) % m;
  }
  return x;
}



enum long MO = 1000000007;
alias Mint = ModInt!MO;

Mint power(Mint a, long e) {
  Mint x = a, y = 1;
  for (; e; e >>= 1) {
    if (e & 1) y *= x;
    x *= x;
  }
  return y;
}

enum L = 2^^18;

int N;
long[] A;

void main() {
  auto fft = new Fft(L);
  auto fft0 = new FFT0(L);
  auto fft1 = new FFT1(L);
  auto fft2 = new FFT2(L);
  
  try {
    for (; ; ) {
      N = readInt();
      A = new long[N];
      foreach (i; 0 .. N) {
        A[i] = readInt();
      }
      
      // auto f = new real[L];
      // f[] = 0.0;
      // foreach (i; 0 .. N) {
        // f[cast(int)(A[i])] += 1;
      // }
      // auto ff = fft.fft!real(f);
      // foreach (l; 0 .. L) {
        // ff[l] = ff[l] * ff[l];
      // }
      // auto g = fft.inverseFft!real(ff);
// pragma(msg,typeof(g));
      
      // foreach (i; 0 .. N) {
        // g[cast(int)(2 * A[i])] -= 1.0;
      // }
      // auto cnt = new long[L];
      // foreach (l; 0 .. L) {
        // cnt[l] = cast(long)(round(g[l].re / 2.0));
      // }
      // debug {
        // writeln("cnt = ", cnt[0 .. 20]);
      // }
      
      auto f = new long[L];
      foreach (i; 0 .. N) {
        ++f[cast(int)(A[i])];
      }
      auto g = convolution(fft0, fft1, fft2, f, f, 2 * (MO - 1));
      foreach (i; 0 .. N) {
        const l = cast(int)(2 * A[i]);
        --g[l];
        if (g[l] < 0) {
          g[l] += 2 * (MO - 1);
        }
      }
      foreach (l; 0 .. L) {
        assert(g[l] % 2 == 0);
        g[l] /= 2;
      }
      debug {
        writeln("g = ", g[0 .. 20]);
      }
      
      Mint ans = 1;
      foreach (l; 0 .. L) {
        ans *= power(Mint(l), g[l]);
      }
      long ASum;
      foreach_reverse (i; 0 .. N) {
        ans *= power(Mint(A[i]), ASum);
        ASum += A[i];
      }
      
      long AMin = long.max;
      auto opt = tuple(real.infinity, 0L, 0L);
      foreach_reverse (i; 0 .. N) {
        if (i < N - 1) {
          chmin(opt, tuple(log(A[i] + AMin) + log(A[i]) * AMin, A[i], AMin));
        }
        chmin(AMin, A[i]);
      }
      debug {
        writeln("opt = ", opt);
      }
      Mint dnm = (opt[1] + opt[2]) * power(Mint(opt[1]), opt[2]);
      ans *= modInv(dnm.x, MO);
      
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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