In a crossover fantasy universe, Houin Kyoma is up in a battle against a powerful monster Nomu that can kill him in a single blow. However being a brilliant scientist Kyoma found a way to pause time for exactly M seconds. Each second, Kyoma attacks Nomu with certain power, which will reduce his health points by that exact power. Initially Nomu has H Health Points. Nomu dies when his Health Points reach 0. Normally Kyoma performs Normal Attack with power A. Besides from Kyoma’s brilliance, luck plays a major role in events of this universe. Kyoma’s Luck L is defined as probability of performing a super attack. A super attack increases power of Normal Attack by C. Given this information calculate and print the probability that Kyoma kills Nomu and survives. If Kyoma dies print “RIP”.
Constraints:
0 < T <= 50
1 <= A, H, C, L1, L2 <= 1000
1 <= M <= 20.
L1<=L2
Input Format:
First line is integer T denoting number of test cases. Each test case consist of single line with space separated numbers A H L1 L2 M C. Where luck L is defined as L1/L2. Other numbers are, as described above.
Output Format:
Print probability that Kyoma kills Nomu in form P1/P2 where P1<=P2 and gcd(P1,P2)=1. If impossible, print “RIP” without quotes.
Example 1
Input:
2
10 33 7 10 3 2
10 999 7 10 3 2
Output:
98/125
RIP
Solution: In Python 3
from math import gcd,factorial
def ncr(n,r):
return factorial(n)/(factorial(n-r)*(factorial(r)))
for i in range(int(input())):
a,h,l1,l2,m,c = [int(i) for i in input().split()]
num = 0
den = pow(l2,m)
if m*(a+c) < h:
print("RIP")
else:
k,z = 0,m*a
while z < h:
z += c
k += 1
for i in range(k,m+1):
if i == 0:
num += pow(l2 - l1,m)
elif i == m:
num += pow(l1,i)
else:
num += (pow(l1,i)*pow(l2-l1,m-i)*ncr(m,i))
x = gcd(int(num),den)
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