Mex Min

AtCoder

IDabc194_e

Time4000ms

Memory256MB

Difficulty—

Let us define $\mathrm{mex}(x_1, x_2, x_3, \dots, x_k)$ as the smallest non-negative integer that does not occur in $x_1, x_2, x_3, \dots, x_k$. You are given an integer sequence of length $N$: $A = (A_1, A_2, A_3, \dots, A_N)$. For each integer $i$ such that $0 \le i \le N - M$, we compute $\mathrm{mex}(A_{i + 1}, A_{i + 2}, A_{i + 3}, \dots, A_{i + M})$. Find the minimum among the results of these $N - M + 1$ computations. ## Constraints * $1 \le M \le N \le 1.5 \times 10^6$ * $0 \le A_i \lt N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ [samples]

Samples

Input #1

3 2
0 0 1

Output #1

1

We have:

*   for $i = 0$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(0, 0) = 1$
*   for $i = 1$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(0, 1) = 2$

Thus, the answer is the minimum among $1$ and $2$, which is $1$.

Input #2

3 2
1 1 1

Output #2

0

We have:

*   for $i = 0$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(1, 1) = 0$
*   for $i = 1$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(1, 1) = 0$

Input #3

3 2
0 1 0

Output #3

2

We have:

*   for $i = 0$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(0, 1) = 2$
*   for $i = 1$: $\mathrm{mex}(A_{i + 1}, A_{i + 2}) = \mathrm{mex}(1, 0) = 2$

Input #4

7 3
0 0 1 2 0 1 0

Output #4

API Response (JSON)

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      "content": "Let us define $\\mathrm{mex}(x_1, x_2, x_3, \\dots, x_k)$ as the smallest non-negative integer that does not occur in $x_1, x_2, x_3, \\dots, x_k$.   You are given an integer sequence of length $N$: $A =",
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      "statement_type": "Markdown",
      "content": "Let us define $\\mathrm{mex}(x_1, x_2, x_3, \\dots, x_k)$ as the smallest non-negative integer that does not occur in $x_1, x_2, x_3, \\dots, x_k$.  \nYou are given an integer sequence of length $N$: $A =...",
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