By | 21.02.2017

# Find the least number for which Proportion of Neutral Numbers is at least n/m

## Increasing, Decreasing & Neutral Numbers

An increasing number is a number in which values of digits increase when we go from left to right; for example,123455 .

Similarly a decreasing number is a number in which values of digits decrease when we go from left to right; for example,54110 .

We shall call a positive integer that is neither increasing nor decreasing a “neutral” number; for example, 151212 .

The count of Neutral numbers increases and by the time we reach 21780 the proportion of neutral numbers >= 90%.

Find the least number for which the proportion of neutral numbers is at least n/m .

## Explanation

### Input Format

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

Each of the following lines contain two integers.

1<=T<10^4

1<=n<m<=10^5

### Output Format

For each of T test cases print one line containing a single integer – the answer to a problem.

2

1 2

90 100

### Sample Output

538

21780

Time Limit:3.0 sec(s) for each input file.

Memory Limit:256 MB

Source Limit:1024 KB

SOURCE CODE : :

```import itertools
def compute(a,b):
count = 0
for i in itertools.count(1):
s = str(i)
t = "".join(sorted(s))
if s != t and s[::-1] != t:
count += 1  # i is neutral
if count * b == a * i:
return str(i)
for i in range(0,input(),1):
a=map(int,raw_input().strip(' ').split())
print(compute(a,a))```

OUTPUT : :

```2

1 5
175

80 100
4770```

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