The tool is now applied to a stress-test string made of a single repeated letter, and must answer: what is the length of the x-th lexicographically smallest distinct piece of that text? Given a string consisting only of the character 'a', repeated N times, and Q queries each giving an integer x, print the length of the x-th lexicographically smallest DISTINCT substring for each query. (This mirrors StringOFaaa directly — derive the closed-form using triangular numbers plus binary search, since N can be up to 10^9.)
Input
Line1: N Q. Next Q lines: one integer x each.
Output
Q lines: length of the x-th smallest substring, or -1 if x exceeds total distinct substrings.
Constraints
1 ≤ N ≤ 10^9, 1 ≤ Q ≤ 10^5, 1 ≤ x ≤ 10^18
Sample Input
4 2 1 5
Sample Output
1 3
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