시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB45216614644.109%

문제

이 문제는 $x_0$와 $N$의 제한을 제외하고 특별한 작은 분수와 같은 문제이다.

NLCS에는 분수가 많다.

분수에서 나오는 물의 높이는 특정한 규칙에 따라 변화하는데, 어떤 정수 시각 $t$에서의 분수의 높이가 정수 $x_t$일 때, $x_{t+1}$는 $x_t$가 짝수라면 $\lfloor \frac{x_t}{2} \rfloor \oplus 6$, $x_t$가 홀수라면 $(2 \cdot x_t) \oplus 6$과 같다.

$0$초에서의 분수의 높이가 주어졌을 때, $N$초에서의 분수의 높이를 구하는 프로그램을 작성하시오.

입력

첫 번째 줄에 $0$초에서의 분수의 높이 $x_0$와 $N$이 주어진다. $x_0$와 $N$은 모두 정수이다.

출력

첫 번째 줄에 $N$초에서의 분수의 높이를 출력한다.

제한

  • $0 \le x_0, N \le 10^{18}$

예제 입력 1

512 2

예제 출력 1

133

예제 입력 2

834390042012203 621527651143931423

예제 출력 2

4

노트

  • $\lfloor x \rfloor$는 $x$보다 작거나 같은 가장 큰 정수를 의미한다.
  • $\oplus$는 비트 XOR 연산을 수행하는 연산자이다. 비트 XOR 연산자에 대한 자세한 정보는 위키백과 (영어)에서 읽을 수 있다. 대부분의 프로그래밍 언어에서 비트 XOR 연산은 ^로 구현되어 있다.
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b2RlPl48XC9jb2RlPi48XC9saT5cclxuPFwvdWw+XHJcbiIsIm9yaWdpbmFsIjoiMCIsImh0bWxfdGl0bGUiOiIwIiwicHJvYmxlbV9sYW5nX3Rjb2RlIjoiRW5nbGlzaCIsImxpbWl0IjoiPHVsPlxyXG5cdDxsaT4kMFxcbGUgeF8wLE4gXFxsZSAxMF57MTh9JDxcL2xpPlxyXG48XC91bD5cclxuIn1d

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