結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー 👑 hos.lyric
提出日時 2019-01-10 16:30:07
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 23 ms / 5,000 ms
コード長 3,129 bytes
コンパイル時間 1,006 ms
コンパイル使用メモリ 118,788 KB
実行使用メモリ 18,688 KB
最終ジャッジ日時 2024-06-13 02:34:13
合計ジャッジ時間 2,561 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 37
権限があれば一括ダウンロードができます

ソースコード

diff # 

import std.conv, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.container, std.math, std.range, 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[0]; tokens.popFront; return token; }
int readInt() { return readToken().to!int; }
long readLong() { return readToken().to!long; }
real readReal() { return readToken().to!real; }

void chmin(T)(ref T t, in T f) { if (t > f) t = f; }
void chmax(T)(ref T t, in T f) { if (t < f) t = f; }

int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; }
int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); }
int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); }


immutable MO = 10L^^9 + 7;

long solve(long[] coef, long[] initial, long e) {
  debug {
    writefln("coef = %s", coef);
    writefln("initial = %s", initial);
    writefln("e = %s", e);
  }
  const n = cast(int)(coef.length) - 1;
  long[] multiply(long[] a, long[] b) {
    auto ret = new long[2 * n];
    foreach (i; 0 .. n) foreach (j; 0 .. n) {
      (ret[i + j] += a[i] * b[j]) %= MO;
    }
    foreach_reverse (i; n .. 2 * n) {
      foreach (k; 1 .. n + 1) {
        (ret[i - k] += coef[k] * ret[i]) %= MO;
      }
    }
    ret.length = n;
    return ret;
  }
  auto x = new long[n];
  auto y = new long[n];
  x[1] = 1;
  y[0] = 1;
  for (; e; e >>= 1) {
    if (e & 1) {
      y = multiply(y, x);
    }
    x = multiply(x, x);
  }
  long ret;
  foreach (i; 0 .. n) {
    (ret += y[i] * initial[i]) %= MO;
  }
  return ret;
}

int N;
long K;
long[] A;

void main() {
  try {
    for (; ; ) {
      N = readInt();
      K = readLong();
      A = new long[N];
      foreach (i; 0 .. N) {
        A[i] = readLong();
      }
      long ansF, ansS;
      if (N <= 10^^4 && K <= 10^^6) {
        auto f = new long[cast(int)(K + 1)];
        auto s = new long[cast(int)(K + 1)];
        foreach (i; 1 .. N + 1) {
          f[i] = A[i - 1];
          s[i] = (s[i - 1] + f[i]) % MO;
        }
        foreach (i; N + 1 .. cast(int)(K) + 1) {
          f[i] = (s[i - 1] - s[i - (N + 1)]) % MO;
          s[i] = (s[i - 1] + f[i]) % MO;
        }
        ansF = f[cast(int)(K)];
        ansS = s[cast(int)(K)];
      } else {
        {
          auto coef = new long[N + 1];
          coef[1 .. N + 1] = 1;
          ansF = solve(coef, A, K - 1);
        }
        {
          auto coef = new long[N + 2];
          coef[1] = 2;
          coef[N + 1] = -1;
          auto ASum = new long[N + 1];
          foreach (i; 0 .. N) {
            ASum[i + 1] = (ASum[i] + A[i]) % MO;
          }
          ansS = solve(coef, ASum, K);
        }
      }
      ansF = (ansF % MO + MO) % MO;
      ansS = (ansS % MO + MO) % MO;
      writeln(ansF, " ", ansS);
    }
  } catch (EOFException e) {
  }
}
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