Nearest Station

I have n tickets for a train with a rabbit. Each ticket is numbered from 0 to n − 1, and you can use the k ticket to go to p⋅ak + q⋅bk station.

Rabbit wants to go to the all-you-can-eat carrot shop at the station m station ahead of the current station, but wants to walk as short as possible. The stations are lined up at regular intervals. When using, how many stations can a rabbit walk to reach the store?

Input

1 ≤ n, m, a, b, p, q ≤ 1 000 000 000 000 (integer)

Output

Output the number of rabbits that can reach the store on foot at the minimum number of stations in one line.

Examples

Input

6 200 2 3 4 5

Output

1

Input

6 1 2 3 4 5

Output

1

inputFormat

Input

1 ≤ n, m, a, b, p, q ≤ 1 000 000 000 000 (integer)

outputFormat

Output

Output the number of rabbits that can reach the store on foot at the minimum number of stations in one line.

Examples

Input

6 200 2 3 4 5

Output

1

Input

6 1 2 3 4 5

Output

1

样例

6 1 2 3 4 5

1