Race

Input

The first line contains two integers $k$ and n~(1 \le k \le 10^9, 1 \le n \le 1000).

The next $n$ lines each contain one integer x~(1 \le x \le 10^5).

Output

Print $n$ lines. Each line should contain a single integer: the minimum number of seconds Bessie needs to travel at least $k$ meters and finish with a speed of at most $x$ meters per second.

Examples

When x = 1, one optimal solution is:

• Increase the speed to $1$ m/s and travel $1$ meter.

• Increase the speed to $2$ m/s and travel $3$ meters in total.

• Keep the speed at $2$ m/s and travel $5$ meters in total.

• Keep the speed at $2$ m/s and travel $7$ meters in total.

• Keep the speed at $2$ m/s and travel $9$ meters in total.

• Decrease the speed to $1$ m/s and travel $10$ meters in total.

When x = 3, one optimal solution is:

• Increase the speed to $1$ m/s and travel $1$ meter.

• Increase the speed to $2$ m/s and travel $3$ meters in total.

• Increase the speed to $3$ m/s and travel $6$ meters in total.

• Keep the speed at $3$ m/s and travel $9$ meters in total.

• Keep the speed at $3$ m/s; the race ends at $10$ meters with a speed of $3$ m/s.

Note that the following is illegal when x = 3:

• Increase the speed to $1$ m/s and travel $1$ meter.

• Increase the speed to $2$ m/s and travel $3$ meters in total.

• Increase the speed to $3$ m/s and travel $6$ meters in total.

• Increase the speed to $4$ m/s and travel $10$ meters in total.

This is because, at the exact moment Bessie reaches $10$ meters, her speed is $4$ m/s, which exceeds the allowed maximum speed of $3$ m/s.