Description

The kth binomial coefficient indexed by n can be calculated by the following relation :
C(n, 0) = 1, for n = 1, 2, …
C(n, 1) = n, for n = 1, 2, …
C(n, n) = 1, for n = 1, 2, …
C(n, k) = C(n-1, k-1) + C(n-1, k),  for k = 2, 3, … and for n = 2, 3, …

Given a nonnegative integer M, display the binomial coefficients indexed by M.
Use '%10d' to print each element. There is no need to print a newline at the end.

Input

A positive integer M (1<=M<=30).

Output

 Print the binomial coefficients indexed by M.

Sample Input  Download

Sample Output  Download

Tags

Discuss

Description

Bob is a businessman. He always stays at city A or city  B.

Assume Bob stays at city A today , and we can use a transition matrix P to infer the probability of at which city will Bob stays tomorrow.

e.g.
Let  Vn^T = [ v_a , v_b ]

V_n is a 2 by 1 column vector.
v_a denotes the probability that Bob stays at city A on n-th day,
v_b denotes the probability that Bob stay at city B on n-th day.

After 1 day, the probability should be represented as V_n+1 , where V_n+1 = P * V_n.

P is a 2 by 2 square matrix, representing the transition probability:

P = ┌ p1  p2 ┐
       └ p3  p4 ┘

---

As time passes, the probability of Bob staying at city A will decrease.

After n days, the probability of Bob staying at city A will smaller than or equal to a target value T.

The question is :

Suppose that Bob stays at city A today ( v_a = 1 , v_b = 0)
How many days do we need to make v_a smaller than or equal to the target value T ?
Namely , n = ?

Note :

The test case will make v_a monotonically decrease .

助教出的測資一定會讓 v_a 隨著時間增加而逐漸遞減

 

Input

There are multiple testcases in the input.

The first line contains a integer N, indicating the number of testcases.

You can use this format in your code:

int i , N;

scanf("%d",&N);

for(i=0;i<N;i++){

      // your code to deal with each testcase

}

The following lines are testcases.

For each testcase, there are 5 floating points in a line.

The 1st ~ 4th floating points (p1, p2, p3, p4) are the elements in trasition matrix P.

The 5th floating point is the target value T.

Output

For each testcase.

Output integer n that tell us how many days should we take to reach the target probability.

And add a '\n' at the end of each output.

 

Sample Input  Download

Sample Output  Download

Tags

Discuss