#### Mr. MMMH and Suborno

**Author: ** QuwsarOhi

Problem Setter:M M Mehedi HasanIntake 33, Department of CSE

Mr. MMMH is a shopkeeper. He sells **n** types of chocolates, from **1** to **n** (1 <= n <= 10^{7}). She has **K** amount of money. She wants to buy the maximum number of **types** of chocolates.

The cost of chocolates are,

The cost of type 1 = The summation of
divisors of 1 = 1.

The cost of type 2 = The summation of
divisors of 2 = 1 + 2 = 3.

The cost of type 3 = The summation of
divisors of 3 = 1 + 3 = 4.

And so onâ€¦.

Check the Input/Output section for further
information.

#### Input Format

You are given two integers **n** (1 <= **n** <= 10^{7}) and **q** (1 <= **q** <= 10^{5}). Here, **n** is the number of types of chocolates, and **q** is the number of test cases.

In each case, you are given one integer **k** (1 <= **k** <= 10^{16}), which is the amount of the money of
Suborno.

#### Output Format

You should find out, the maximum number
of types of chocolates she can buy using **k**
amount of money from **1** to **n** types of chocolates under the
above-illustrated cost conditions.

#### Samples

###### Input

###### Output

Language | Time | Memory |

GNU C 11 | 5s | 512MB |

GNU C++ 14 | 5s | 512MB |

GNU C++ 11 | 5s | 512MB |