Exceeding Z

Source: beecrowd

Version: Phuoc Hung OJ Extended

Problem Statement

Read integer X, then successive candidates for Z. Discard candidates Z <= X and select the first Z > X. Add consecutive integers X, X+1, X+2, ... until the sum is strictly greater than Z. Print the minimum number of terms.

Input

The first integer is X, followed by candidates for Z until the first one greater than X, inclusive.

Output

Print the smallest count of consecutive terms whose sum exceeds Z.

Subtasks

• Subtask 1 (20%): 1<=X<=10, each candidate Z in [-100,100], at most 5 candidates.
• Subtask 2 (30%): -20<=X<=50, candidates in [-10000,10000], at most 20.
• Subtask 3 (50%): -1000<=X<=1000, candidates in [-1000000,1000000], at most 100.

Examples

Example 1

Input

3
1
20

Output

5

Explanation

Ignore Z=1. Partial sums for 3,4,5,6,7 are 3,7,12,18,25; the fifth first exceeds 20.

Example 2

Input

21
21
15
30

Output

2

Explanation

Candidates 21 and 15 are invalid. 21 alone does not exceed 30, while 21+22=43 does.