Divisor Count#7317

Divisor Count

3 seconds
128 megabytes
Hard

Find the first positive integers that have exactly divisors.

Definition. A divisor of an integer is an integer such that the ratio is also an integer.

Given and , find the first positive integers not exceeding 10^{18} that have exactly distinct divisors. If the total number of such numbers is less than , you must print all of them.

Input

Two integers and k~(1 \le n, k \le 110000) — the number of required numbers and the required number of divisors.

Output

Print numbers, one per line: the first positive integers not exceeding 10^{18} that have exactly distinct divisors, in ascending order.

If there are only m < n such numbers, then for each of the remaining n - m lines print .

Examples

Example 1

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Example 2

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