Of course, many of you can calculate φ(*n*) — the number of positive integers that are less than or equal to *n*, that are coprime with *n*. But what if we need to calculate φ(φ(...φ(*n*))), where function φ is taken *k* times and *n* is given in the canonical decomposition into prime factors? 

You are given *n* and *k*, calculate the value of φ(φ(...φ(*n*))). Print the result in the canonical decomposition into prime factors.
The first line contains integer *m* (1 ≤ *m* ≤ 10<sup class="upper-index">5</sup>) — the number of distinct prime divisors in the canonical representaion of *n*.

Each of the next *m* lines contains a pair of space-separated integers *p*<sub class="lower-index">*i*</sub>, *a*<sub class="lower-index">*i*</sub> (2 ≤ *p*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">6</sup>; 1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">17</sup>) — another prime divisor of number *n* and its power in the canonical representation. The sum of all *a*<sub class="lower-index">*i*</sub> doesn't exceed 10<sup class="upper-index">17</sup>. Prime divisors in the input follow in the strictly increasing order.

The last line contains integer *k* (1 ≤ *k* ≤ 10<sup class="upper-index">18</sup>).
print("_RANDOM_GUESS_1689443903.8613033")# 1689443903.8613245