Consider a number X on which K Mag-Inc operations are to be performed. In a Mag-Inc operation, the number X undergoes an increment of A/B times of X where A and B are two integers.

There is a numerator and a denominator array of size K which contain the ith values of A and B. After K Mag-Inc operations, the number X turns to M.

Now your job is to find what percentage of M is to be decremented from M if it has to be converted back to X. Let this percentage be denoted by Z.

Print the integral part of Z.

-----Input:-----

First line contains an integer T denoting the number of test cases.

First line of every test case contains two space separated integers X and K.

The second and third line of every test case will contain K space separated integers 

denoting the Numerator and Denominator array.

-----Output:-----

For each test case, print the required result in a single line.

-----Constraints:-----
1 ≤ T ≤ 100
1 ≤ K, A, B ≤ 40000
1≤X≤10^100

-----Example:-----Input:
2
100 1
1 
4
100 2
1 1
2 3Output:
20
50

-----Explanation:-----

Case 2: 100 undergoes an increment of (1/2)*100. Therefore M = 100 + 50.

Now M = 150.

Now again, 

M undergoes an increment of (1/3)*150. Therefore, M = 150 + 50. 

Now as we want to revert back M = 200 to X i.e. 100, we need to decrement it by a value 

of 100 and we know that 100 is 50% of 200.

Hence, we print 50.

Difficulty: interview

Starter code:

Solutions:
import sys
import math

def solution():
 T = int(input().strip())
 for _ in range(T):
  x, k = list(map(float, input().strip().split(' ')))
  original_x = x
  if k == 1:
   a = [float(input().strip())]
   b = [float(input().strip())]
  else:
   a = list(map(float, input().strip().split(' ')))
   b = list(map(float, input().strip().split(' ')))
  for i in range(int(k)):
   x = x + (a[i]/b[i])*(x)
  percentage = ((x - original_x) / x)*100
  print("%d"%(int(percentage)))

solution()

import sys
T=int(sys.stdin.readline())
while T:
 n,k=list(map(int,input().split()))
 num=list(map(int, sys.stdin.readline().split()))
 den=list(map(int, sys.stdin.readline().split()))
 ans=n
 for i in range (k):
  ans+=ans*num[i]/float(den[i])
 print(int(100-100*n/ans))
 T-=1

t = int(input())

for i in range(t):
 value, k = list(map(int, input().split()))
 A = list(map(int, input().split()))
 B = list(map(int, input().split()))
 newValue = value
 for j in range(k):
  temp = newValue*float(A[j])/B[j]
  newValue+=temp
 error = value*100/newValue
 print(int(100-error))


t=int(input())
for tc in range(0,t):
 n,k=list(map(int,input().split()))
 num=list(map(int,input().split()))
 den=list(map(int,input().split()))
 temp=n
 for i in range(0,k):
  temp=temp+(temp**1.0*num[i]/den[i])
 answer=int(100-(n*1.0*100/temp))
 print(answer)

t=eval(input())
while t:
 t-=1
 x,k=list(map(int,input().split()))
 a=list(map(float,input().split()))
 b=list(map(float,input().split()))
 rat = 1.0
 for i in range(k):
  rat = rat*((a[i]+b[i])/b[i])
 rat = ((rat-1)/rat)*100.0
 print(int(rat))


t = float(input())
while(t):
 t -= 1
 x, k = list(map(float, input().split()))
 k = int(k)
 a = list(map(float, input().split()))
 b = list(map(float, input().split()))
 temp = x
 for i in range(0, k):
  xxx = (temp*a[i])/b[i]
  temp += xxx
 px = (temp-x)/temp * 100.0;
 print(int(px)) 

for _i in range(int(input())):
 x,k = list(map(int,input().split()))
 a = list(map(int,input().split()))
 b = list(map(int,input().split()))
 l = []
 l.append(x)
 for i in range(k):
  x = x+(x*(float(a[i])/b[i]))
 w = l[0]
 perc = 100*(float(w)/x)
 ans = 100-perc
 print(int(ans))