By | 18.02.2017

# WAP to Print number of not neutral numbers below 10^k mod(10^9+7)

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 . Python is an high-level language We shall call a positive integer that is neither increasing nor decreasing a “neutral” number; for example, 151212 . As n increases, the proportion of neutral numbers below n increases such that there are 12951 numbers below one-million that are not neutral and only 277032 non-neutral numbers below 10^10.

How many numbers below 10^k are not neutral? Print the number of not neutral numbers below 10^k mod(10^9+7).

## Explanation

Input Format

First line contains an integer T which is the number of tests, next T lines contain an integer .

CONSTRAINTS

1<=T<=7

3<=k<=10

Sample Input :

3

3

5

10

Sample Output :

474

4953

277032

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

Memory Limit:256 MB

Source Limit:1024 Kb

## SOURCE CODE ::

```import math
def binomial(n, k):
assert 0 <= k <= n
return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))
def compute(a):
DIGITS = a
increasing = binomial(DIGITS + 9, 9) - 1
decreasing = binomial(DIGITS + 10, 10) - (DIGITS + 1)
flat = DIGITS * 9
ans = (increasing + decreasing - flat)
return str(ans)
a=input()
for i in range(0,a,1):
print(compute(input()))```

## OUTPUT : :

```//First Run---------------------------------------------------

3

3
474

5
4953

10
277032

//Second Run---------------------------------------------

3

4
1674

20
40059818

100
51161058134250```

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My name is Tunde Ajetomobi, a Tech Enthusiast and Growth Hacker. I enjoy creating helpful content that solves problem across different topics. Codezclub is my way of helping young aspiring programmers and students to hone their skills and find solutions on fundamental programming languages.

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