Bacteria

Bacteria, which are microscopic and predominantly unicellular organisms, are one of the primary groups of living organisms. We are observing a colony consisting of n bacteria. Each bacterium in this species dies after three days. Every day, the colony grows by b percent, calculated as the largest integer k such that the inequality b >= k * 100 / n is satisfied.

Your task is to determine the number of days the colony will continue to exist. If this number exceeds 1000, you should output the word live.

Input

Two integers, n and b.

Output

A single integer representing the number of days the colony survives (up to the day the last bacterium dies) or the word live.

Examples

Note

For example, if n=10 and b=25:

• On the first day, the colony grows by 25% of 10, which is 2, resulting in a total of 12 bacteria.

• On the second day, it grows by 25% of 12, which is 3, bringing the total to 15.

• On the third day, it grows by 25% of 15, which is 3. After 10 bacteria die, the total becomes 15 + 3 - 10 = 8.

The process continues in this manner.