Final and Minimum Balance

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Start from balance b. Each transaction type 1 adds x and type 2 subtracts x. Output final balance and minimum across the initial and every post-transaction balance; negative balances remain valid.

Input

First n b, followed by n pairs type and amount.

Output

Print final_balance minimum_balance.

Subtasks

• Subtask 1 (20%): n ≤ 20, amounts/balance ≤100.

• Subtask 2 (30%): n ≤ 1000, amounts/balance ≤10^6.

• Subtask 3 (50%): n ≤ 100000, amounts/balance ≤10^9.

Examples

Example 1

Input:

3 10
1 5
2 20
1 2

Output:

-3 -5

Explanation: Balances are 10,15,-5,-3, hence final -3 and minimum -5.

Example 2

Input:

0 7

Output:

7 7

Explanation: With no transaction both balances equal the initial balance.