Problem Statement

Takahashi is an apprentice wizard, training to decipher formulas inscribed on magic circles. The magic circles have mathematical expressions written in Polish notation (prefix notation).

Polish notation is a notation where operators are placed before their operands. All operators handled here are the 4 types of binary operators: +, -, *, /. A Polish notation expression is recursively defined as follows:

• A single integer is a Polish notation expression, and its evaluation result is that integer itself.
• op A B (where op is a binary operator, and A and B are each Polish notation expressions) is also a Polish notation expression, and its evaluation result is the result of applying operator op to the evaluation results of A and B.

Division / is truncated division toward zero. That is, the fractional part of the quotient as a real number is discarded, and the integer closer to 0 is taken as the result (e.g., 7 / 2 = 3, (-7) / 2 = -3, 7 / (-2) = -3).

For example, the expression written as (3 + 5) * 2 in standard infix notation is represented as * + 3 5 2 in Polish notation. This expression consists of 5 tokens *, +, 3, 5, 2, and its evaluation result is 16.

An expression is given as a sequence of tokens (strings representing operators or integers). A token is an operator if and only if it is a 1-character string that exactly matches one of +, -, *, /. All other tokens represent integers. For example, -3 consists of 2 characters and does not match any of +, -, *, /, so it is not an operator but represents the integer -3. On the other hand, when the token - appears alone (as a 1-character string), it always means the subtraction operator and is never interpreted as a negative sign.

Tokens representing integers are given in decimal notation. For negative integers, a negative sign - is prepended. The part excluding the negative sign does not contain unnecessary leading 0s (however, the token representing the integer 0 is the single character 0). The token -0 is never given.

One day, Takahashi discovered an ancient magic circle and tried to decipher the Polish notation expression inscribed on it. However, the mischievous Aoki cast an inversion curse on the magic circle, replacing some operators with their paired operators. Specifically, Aoki chose K distinct positions (1-indexed) from the token sequence. The token at each chosen position is guaranteed to be an operator, and Aoki performed the following replacements on each:

• + is replaced with -, and - is replaced with +
• * is replaced with /, and / is replaced with *

Takahashi wants to know both the evaluation result of the original expression before the curse and the evaluation result of the expression after the curse.

You are given a sequence of N tokens t_1, t_2, \ldots, t_N constituting the original Polish notation expression, and K integers p_1, p_2, \ldots, p_K representing the positions of the operators that Aoki inverted. Compute the evaluation result of the original expression and the evaluation result of the inverted expression, respectively.

Constraints

• 1 \leq N \leq 2 \times 10^5
• N is odd
• The token sequence t_1, t_2, \ldots, t_N constitutes a valid Polish notation expression
• Each token t_i is either an operator (a 1-character string exactly matching one of +, -, *, /) or a string representing an integer
• The absolute value of the integer represented by each integer token is at most 10^9
• 0 \leq K \leq N
• 1 \leq p_i \leq N (1 \leq i \leq K)
• p_1, p_2, \ldots, p_K are all distinct
• The token t_{p_i} at each position p_i is an operator
• No division by 0 occurs during the evaluation of either the original or inverted expression
• The absolute value of the evaluation result of every subexpression (both intermediate and final results) appearing during the evaluation of either the original or inverted expression is at most 10^{18}

Sample Input 1

5
* + 3 5 2
1
1

Sample Output 1

16
4

Sample Input 2

3
/ -7 2
1
1

Sample Output 2

-3
-14

Sample Input 3

21
+ / + * -8 3 7 - 10 2 * - / 20 3 -5 + * 2 -3 4
5
1 2 4 11 18

Sample Output 3

-24
38

Sample Input 4

31
- * - + 5 1 * 2 3 + / 21 3 - 9 2 / - * 7 2 + 1 3 * - 9 4 / 50 5
7
1 4 7 11 17 25 29

Sample Output 4

0
280

Sample Input 5

1
-1000000000
0

Sample Output 5

-1000000000
-1000000000