SDE - 1

Ninja has a number ‘A’ containing ‘B’ digits. ‘A’ can be represented by a string ‘S’ where ‘S[i]’ denotes the ‘ith’ digit of ‘A’. You are also given an integer ‘K’.

Ninja thinks that a number is stable if the following condition is satisfied:

For every ‘ith’ digit where (0 <= ‘i’ <= ‘B-1’) ‘S[i] = S[i%K]’. Here, ‘X%Y’ represents the modulo operations. The remainder when ‘X’ is divided by ‘Y’.

Your task is to find the smallest number which is stable and whose value is greater than or equal to ‘A’. Zero-based indexing is used everywhere.

Example :

‘B’ = 4, ‘S’ = “4321”, ‘K’ = 3.
The given number is not stable as ‘S[3]’ is not the same as ‘S[0]’ but 3%3 = 0 same as 0%3. ‘S[3] = 1’ and ‘S[0] = 4’.  But the number “4324” is stable. As, for all ‘i’, ‘S[i]’ = ‘S[i%K]’ and “4324” is also greater than the given number. It can be proved that this is the best possible answer.
Hence, the answer is “4324”.

Given an array “A” of N integers and you have also defined the new array “B” as a concatenation of array “A” for an infinite number of times.

For example, if the given array “A” is [1,2,3] then, infinite array “B” is [1,2,3,1,2,3,1,2,3,.......].

Now you are given Q queries, each query consists of two integers “L“ and “R”(1-based indexing). Your task is to find the sum of the subarray from index “L” to “R” (both inclusive) in the infinite array “B” for each query.

Note :

The value of the sum can be very large, return the answer as modulus 10^9+7.

You are given 4 arrays 'ARR1’, 'ARR2’, 'ARR3’, 'ARR4’, each consists of ‘N’ numbers. Your task is to return the number of tuples (i, j, k, l) satisfying the following conditions:

0 <= i,j,k,l < ‘N’
ARR1[i] + ARR2[j] + ARR3[k] + ARR4[l] = 0.

There are 'N' students standing in a line, and their heights are given. But the constraint is that the difference in heights of adjacent students does not exceed 'K', i.e.,

| height[i] - height[i+1] | <= K, where i ∈  (1, N-1)

Your task is to find the position of a student having height 'H'. If no such student is found, return -1.

Note:

Positions are counted starting from 0.
If two or more students have height equal to 'H', return the student with the minimum position.

You are given an array ‘Arr’ of ‘N’ integers. Your task is to reduce each of the elements to zero. You can perform the following two operations on the array. Select an index ‘i’. If ‘Arr[i]’ is odd then replace it with ‘(Arr[i]-1) / 2’ else replace it with ‘Arr[i] / 2’.

Return the total number of operations required to reduce each element of the array to zero.

Example:

‘N’=5, ‘Arr’ = [2 , 5 , 6 , 3 , 1].
2 -> 1 -> 0
5 -> 2 -> 1 -> 0
6 -> 3 -> 1 -> 0
3 -> 1 -> 0
1 -> 0

Hence total operations will be 11.

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