Range Sort Query

AtCoder

IDabc237_g

Time8000ms

Memory256MB

Difficulty—

Given is a permutation $P=(P_1,P_2,\ldots,P_N)$ of $1,2,\ldots,N$, and an integer $X$. Additionally, $Q$ queries are given. The $i$\-th query is represented as a triple of numbers $(C_i,L_i,R_i)$. Each query does the following operation on the permutation $P$. * If $C_i=1$: sort $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ in ascending order. * If $C_i=2$: sort $P_{L_i},P_{L_i+1},\ldots,P_{R_i}$ in descending order. In the final permutation $P$ after executing all queries in the given order, find $i$ such that $P_i=X$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq Q \leq 2\times 10^5$ * $1 \leq X \leq N$ * $(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$. * $1 \leq C_i \leq 2$ * $1 \leq L_i \leq R_i \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $X$ $P_1$ $P_2$ $\ldots$ $P_N$ $C_1$ $L_1$ $R_1$ $C_2$ $L_2$ $R_2$ $\vdots$ $C_Q$ $L_Q$ $R_Q$ [samples]

Samples

Input #1

Output #1

3

Initially, the permutation is $P=[1,4,5,2,3]$. The queries change it as follows.

*   $1$\-st query sorts the $3$\-rd through $5$\-th elements in ascending order, making $P=[1,4,2,3,5]$.
*   $2$\-nd query sorts the $1$\-st through $3$\-rd elements in descending order, making $P=[4,2,1,3,5]$.

In the final permutation, we have $P_3=1$, so $3$ should be printed.

Input #2

7 3 3
7 5 3 1 2 4 6
1 1 7
2 3 6
2 5 7

Output #2

7

The final permutation is $P=[1,2,6,5,7,4,3]$.

API Response (JSON)

{
  "problem": {
    "name": "Range Sort Query",
    "description": {
      "content": "Given is a permutation $P=(P_1,P_2,\\ldots,P_N)$ of $1,2,\\ldots,N$, and an integer $X$. Additionally, $Q$ queries are given. The $i$\\-th query is represented as a triple of numbers $(C_i,L_i,R_i)$. Eac",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 8000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc237_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a permutation $P=(P_1,P_2,\\ldots,P_N)$ of $1,2,\\ldots,N$, and an integer $X$.\nAdditionally, $Q$ queries are given. The $i$\\-th query is represented as a triple of numbers $(C_i,L_i,R_i)$. Eac...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments