Grimm's Conjecture

Grimm's conjecture states that whenever you are given a block of consecutive composite numbers, you can assign to each of them a distinct prime that divides it.

Formally, if $n+1, n+2, \dots, n+k$ are all composite, then there exist $k$ distinct primes $p_i$ such that $p_i$ divides $n+i$. ($1 \le i \le k$)

Given an interval $[L, H]$ of consecutive composite numbers, write a program that, for each of $L, L+1, \dots, H$, finds one distinct prime dividing it.

If several assignments are possible, output the lexicographically smallest one: make the prime assigned to the first number as small as possible; among those, make the prime assigned to the second number as small as possible; then the third, and so on.

The input consists of several test cases. Each test case is a single line with two integers $L$ and $H$. ($4 \le L < H \le 10^{10}$)

Every number in the interval $[L, H]$ is guaranteed to be composite.

The last line contains two zeros and must not be processed.

For each test case, print on one line the prime assigned to each number from $L$ to $H$, separated by single spaces.