Linear Probing

AtCoder

IDabc228_d

Time4000ms

Memory256MB

Difficulty—

There is a sequence $A = (A_0, A_1, \dots, A_{N - 1})$ with $N = 2^{20}$ terms. Initially, every term is $-1$. Process $Q$ queries in order. The $i$\-th query $(1 \leq i \leq Q)$ is described by an integer $t_i$ such that $t_i = 1$ or $t_i = 2$, and another integer $x_i$, as follows. * If $t_i = 1$, do the following in order. 1. Define an integer $h$ as $h = x_i$. 2. While $A_{h \bmod N} \neq -1$, keep adding $1$ to $h$. We can prove that this process ends after finite iterations under the Constraints of this problem. 3. Replace the value of $A_{h \bmod N}$ with $x_i$. * If $t_i = 2$, print the value of $A_{x_i \bmod N}$ at that time. Here, for integers $a$ and $b$, $a \bmod b$ denotes the remainder when $a$ is divided by $b$. ## Constraints * $1 \leq Q \leq 2 \times 10^5$ * $t_i \in { 1, 2 } \, (1 \leq i \leq Q)$ * $0 \leq x_i \leq 10^{18} \, (1 \leq i \leq Q)$ * There is at least one $i$ $(1 \leq i \leq Q)$ such that $t_i = 2$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $Q$ $t_1$ $x_1$ $\vdots$ $t_{Q}$ $x_{Q}$ [samples]

Samples

Input #1

Output #1

1048577
-1

We have $x_1 \bmod N = 1$, so the first query sets $A_1 = 1048577$.
In the second query, initially we have $h = x_2$, for which $A_{h \bmod N} = A_{1} \neq -1$, so we add $1$ to $h$. Now we have $A_{h \bmod N} = A_{2} = -1$, so this query sets $A_2 = 1$.
In the third query, we print $A_{x_3 \bmod N} = A_{1} = 1048577$.
In the fourth query, we print $A_{x_4 \bmod N} = A_{3} = -1$.
Note that, in this problem, $N = 2^{20} = 1048576$ is a constant and not given in input.

API Response (JSON)

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