Associate Software Engineer

You are given two non-negative numbers 'num1' and 'num2' represented in the form of linked lists.

The digits in the linked lists are stored in reverse order, i.e. starting from least significant digit (LSD) to the most significant digit (MSD), and each of their nodes contains a single digit.

Calculate the sum of the two numbers and return the head of the sum list.

Example :

Input:
'num1' : 1 -> 2 -> 3 -> NULL
'num2' : 4 -> 5 -> 6 -> NULL

Output: 5 -> 7 -> 9 -> NULL

Explanation: 'num1' represents the number 321 and 'num2' represents 654. Their sum is 975.

Axel and Shawn just finished their football practice and are now tired, so they can’t go back and play football, but they have come up with a new game to make the best out of their time.

There are two rooms, one of the rooms has ‘N’ baskets and the other has ‘M’ baskets, each basket is large enough to hold multiple footballs. In each turn, a player has to select a basket from their respective room and pick up some positive number of football(s), the player loses if he is not able to pick up any football.

In each round Axel plays the first turn and Shawn plays the second one. Both Axel and Shawn should be in different rooms when the round starts. Before the start of each round, you can decide the room each player is assigned. Axel is your close friend and you will try your best to make Axel win the game. Predict the winner if both the players play optimally and you try your best to make Axel win the game.

For Example :

If room1: {1, 2, 3} and room2: {1, 1}

Then, Axel will be assigned room1 at the beginning of each round, and both Shawn and Axel will pick only one football in each round as they play optimally, this will result in Shawn exhausting the remaining balls in room2 early, and ultimately losing the game.

Ninja has organized the new year party and invited all the programmers for it, as being the programmer also has been invited by Ninja.

To detect whether the guest is a programmer or not, Ninja has set some tasks for them, such that only programmers can code them.

You have also been asked to solve and code the following task to verify your identity.

Given two integers, 'N' and 'K' find the number of permutation arrays of 'N' integers from 0 to 'N' - 1 satisfying the below condition.

There should be at least 'K' positions in the array such that 'ARR[I] = I' ( 0 <= I < N ) satisfies.

You are required to output the answer modulo 10^9 +7.

EXAMPLE:

Input: 'N' = 4 'K' = 3 
Output: 1

There is only one permutation [0, 1, 2, 3] such that a number of elements with 'ARR[I] = I' is 'K' = 3.

Interviewer given me a problem that how many times we can subtract 5 from 35.