For a positive integer n and parameters a, b, c, p, q, define on x > 0 the function

f_n(x) = a * exp(-x) * cos(b*x) * cos(x/n) + c * n^p * x^q * exp(-n*x)

Let I_n be the integral of f_n(x) over (0, infinity). For every query, I_n is finite for each n. Compute

L = limit of I_n as n -> infinity

or determine that the limit is not finite.

Input

The first line contains the integer T, the number of queries. Each of the next T lines contains a, b, c (real numbers with at most 6 digits after the decimal point) and p, q (integers), separated by spaces.

Output

T lines. On line i, print L for query i with absolute or relative error at most 1e-9, or the string DIVERGES if the limit is not finite.

Constraints

1 <= T <= 10000

|a|, |c| <= 10

|b| <= 5

0 <= p <= 10

0 <= q <= 8

Example

Input:

4
2.5 0 0 3 2
0 1 3 1 0
1 2 4 2 2
1 1 -2 4 1

Output:

2.5
3.0
0.2
DIVERGES

Scoring

This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.