Pirates and coins

Time limit 1 second

Memory limit 128 MiB

npirates fairly divided the treasure of m gold coins - everyone got his part according to their rank and seniority pirate. Youngest pirate took a coin and each pirate taking on the next one coin more than the previous colleague. The last was the captain, who got twice as much of the plan, it is obvious that after the coins are no more.

How many pirates along with the captain, if we know a and m. Since the captain without a team just a pirate, then n > 1.

Input data

Two positive integers a and m (1 ≤ a ≤ 100, m < 15150). Input values are correct.

Output data

The number of pirates n.

Examples

Input example #1

5 25

Output example #1