[Solution] Maximise Set Bits CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Maximise Set Bits CodeChef Solution | CodeChef Problem Solution 2022

Let f(X)$f(X)$ denote the number of set bits in X$X$.

Given integers N$N$ and K$K$, construct an array A$A$ of length N$N$ such that:

• 0≤Ai≤K$0\le A_i\le K$ for all (1≤i≤N)$(1\le i\le N)$;
• ∑Ni=1Ai=K$\sum _{i=1}^N{A}_i=K$

Over all such possible arrays, find the maximum value of ∑Ni=1f(Ai)$\sum _{i=1}^{N}f(A_i)$.

Input Format

• The first line of input contains a single integer T$T$ - the number of test cases. The description of T$T$ test cases follow.

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• The only line of each test case contains integers N$N$ and K$K$- the length of the array and sum of elements respectively.

Output Format

For each test case, output the maximum value of ∑Ni=1f(Ai)$\sum _{i=1}^{N}f(A_i)$.

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Constraints

• 1≤T≤104$1\le T\le {10}^4$
• 1≤N≤109$1\le N\le {10}^9$
• 0≤K≤10