Planarian Regeneration

Notes

For this problem, it is recommended to use floating point numbers, which are more accurate than double.

Input

m n x k l y

For input, six integers m, n, x, k, l, y are given in the above input format. These six integers correspond to those in the problem statement, repeating the horizontal m: n cut x times and the vertical k: l cut y times. 1 ≤ m, n, k, l ≤ 100, 0 ≤ x, y ≤ 40, and m, n and l, k are relatively prime.

Output

Print out the expected number of planarians that are regenerating to their original form after a few weeks in a row. The output is acceptable with an error of 10-6 or less.

Examples

Input

1 1 1 1 1 1

Output

0.562500

Input

1 2 2 1 1 1

Output

0.490741

Input

1 2 0 3 4 0

Output

1.000000

inputFormat

Input

m n x k l y

For input, six integers m, n, x, k, l, y are given in the above input format. These six integers correspond to those in the problem statement, repeating the horizontal m: n cut x times and the vertical k: l cut y times. 1 ≤ m, n, k, l ≤ 100, 0 ≤ x, y ≤ 40, and m, n and l, k are relatively prime.

outputFormat

Output

Print out the expected number of planarians that are regenerating to their original form after a few weeks in a row. The output is acceptable with an error of 10-6 or less.

Examples

Input

1 1 1 1 1 1

Output

0.562500

Input

1 2 2 1 1 1

Output

0.490741

Input

1 2 0 3 4 0

Output

1.000000

样例

1 2 2
1 1 1

0.490741