E - Filters

Score : $500$ points

Problem Statement

Given are integer sequences $A = (a_1, a_2, \dots, a_N)$, $T = (t_1, t_2, \dots, t_N)$, and $X = (x_1, x_2, \dots, x_Q)$.
Let us define $N$ functions $f_1(x), f_2(x), \dots, f_N(x)$ as follows:

$f_i(x) = \begin{cases} x + a_i & (t_i = 1)\\ \max(x, a_i) & (t_i = 2)\\ \min(x, a_i) & (t_i = 3)\\ \end{cases}$

For each $i = 1, 2, \dots, Q$, find $f_N( \dots f_2(f_1(x_i)) \dots )$.

Constraints

• All values in input are integers.
• $1 ≤ N ≤ 2 \times 10^5$
• $1 ≤ Q ≤ 2 \times 10^5$
• $|a_i| ≤ 10^9$
• $1 ≤ t_i ≤ 3$
• $|x_i| ≤ 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $t_1$

$a_2$ $t_2$

$\vdots$

$a_N$ $t_N$

$Q$

$x_1$ $x_2$ $\cdots$ $x_Q$

Output

Print $Q$ lines. The $i$-th line should contain $f_N( \dots f_2(f_1(x_i)) \dots )$.

3
-10 2
10 1
10 3
5
-15 -10 -5 0 5

0
0
5
10
10

We have $f_1(x) = \max(x, -10), f_2(x) = x + 10, f_3(x) = \min(x, 10)$, thus:

• $f_3(f_2(f_1(-15))) = 0$
• $f_3(f_2(f_1(-10))) = 0$
• $f_3(f_2(f_1(-5))) = 5$
• $f_3(f_2(f_1(0))) = 10$
• $f_3(f_2(f_1(5))) = 10$