Cheating Amidakuji

AtCoder

IDabc279_e

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of length $M$ consisting of integers between $1$ and $N-1$, inclusive: $A=(A_1,A_2,\dots,A_M)$. Answer the following question for $i=1, 2, \dots, M$. * There is a sequence $B=(B_1,B_2,\dots,B_N)$. Initially, we have $B_j=j$ for each $j$. Let us perform the following operation for $k=1, 2, \dots, i-1, i+1, \dots, M$ in this order (in other words, for integers $k$ between $1$ and $M$ except $i$ in ascending order). * Swap the values of $B_{A_k}$ and $B_{A_k+1}$. * After all the operations, let $S_i$ be the value of $j$ such that $B_j=1$. Find $S_i$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq M \leq 2\times 10^5$ * $1 \leq A_i \leq N-1\ (1\leq i \leq M)$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_M$ [samples]

Samples

Input #1

5 4
1 2 3 2

Output #1

1
3
2
4

For $i = 2$, the operations change $B$ as follows.

*   Initially, $B = (1,2,3,4,5)$.
*   Perform the operation for $k=1$. That is, swap the values of $B_1$ and $B_2$, making $B = (2,1,3,4,5)$.
*   Perform the operation for $k=3$. That is, swap the values of $B_3$ and $B_4$, making $B = (2,1,4,3,5)$.
*   Perform the operation for $k=4$. That is, swap the values of $B_2$ and $B_3$, making $B = (2,4,1,3,5)$.

After all the operations, we have $B_3=1$, so $S_2 = 3$.
Similarly, we have the following.

*   For $i=1$: performing the operation for $k=2,3,4$ in this order makes $B=(1,4,3,2,5)$, so $S_1=1$.
*   For $i=3$: performing the operation for $k=1,2,4$ in this order makes $B=(2,1,3,4,5)$, so $S_3=2$.
*   For $i=4$: performing the operation for $k=1,2,3$ in this order makes $B=(2,3,4,1,5)$, so $S_4=4$.

Input #2

3 3
2 2 2

Output #2

1
1
1

Input #3

10 10
1 1 1 9 4 4 2 1 3 3

Output #3

API Response (JSON)

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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a sequence of length $M$ consisting of integers between $1$ and $N-1$, inclusive: $A=(A_1,A_2,\\dots,A_M)$. Answer the following question for $i=1, 2, \\dots, M$.\n\n*   There is a sequence ...",
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