Many Operations

AtCoder

IDabc261_e

Time2000ms

Memory256MB

Difficulty—

We have a variable $X$ and $N$ kinds of operations that change the value of $X$. Operation $i$ is represented as a pair of integers $(T_i,A_i)$, and is the following operation: * if $T_i=1$, it replaces the value of $X$ with $X\ {\rm and}\ A_i$; * if $T_i=2$, it replaces the value of $X$ with $X\ {\rm or}\ A_i$; * if $T_i=3$, it replaces the value of $X$ with $X\ {\rm xor}\ A_i$. Initialize $X$ with the value of $C$ and execute the following procedures in order: * Perform Operation $1$, and then print the resulting value of $X$. * Next, perform Operation $1, 2$ in this order, and then print the value of $X$. * Next, perform Operation $1, 2, 3$ in this order, and then print the value of $X$. * $\vdots$ * Next, perform Operation $1, 2, \ldots, N$ in this order, and then print the value of $X$. What are ${\rm and}, {\rm or}, {\rm xor}$?The ${\rm and}, {\rm or}, {\rm xor}$ of non-negative integers $A$ and $B$ are defined as follows: * When $A\ {\rm and}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if both of the digits in that place of $A$ and $B$ are $1$, and $0$ otherwise. * When $A\ {\rm or}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if at least one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise. * When $A\ {\rm xor}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise. For example, $3\ {\rm and}\ 5 = 1$, $3\ {\rm or}\ 5 = 7$, and $3\ {\rm xor}\ 5 = 6$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1\leq T_i \leq 3$ * $0\leq A_i \lt 2^{30}$ * $0\leq C \lt 2^{30}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $C$ $T_1$ $A_1$ $T_2$ $A_2$ $\vdots$ $T_N$ $A_N$ [samples]

Samples

Input #1

Output #1

9
15
12

The initial value of $X$ is $10$.

*   Operation $1$ changes $X$ to $9$.
*   Next, Operation $1$ changes $X$ to $10$, and then Operation $2$ changes it to $15$.
*   Next, Operation $1$ changes $X$ to $12$, and then Operation $2$ changes it to $13$, and then Operation $3$ changes it to $12$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Many Operations",
    "description": {
      "content": "We have a variable $X$ and $N$ kinds of operations that change the value of $X$. Operation $i$ is represented as a pair of integers $(T_i,A_i)$, and is the following operation: *   if $T_i=1$, it rep",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc261_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a variable $X$ and $N$ kinds of operations that change the value of $X$. Operation $i$ is represented as a pair of integers $(T_i,A_i)$, and is the following operation:\n\n*   if $T_i=1$, it rep...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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