import std.conv, std.functional, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.range, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


enum MO = 10L^^9 + 7;

int N, K;
long[] A;

void main() {
  try {
    for (; ; ) {
      N = readInt();
      K = readInt();
      A = new long[N];
      foreach (i; 0 .. N) {
        A[i] = readLong();
      }
      
      int[][long] pes;
      foreach (i; 0 .. N) {
        long a = A[i];
        for (long p = 2; p * p <= a; ++p) {
          if (a % p == 0) {
            int e;
            do {
              ++e;
              a /= p;
            } while (a % p == 0);
            pes[p] ~= e;
          }
        }
        if (a > 1) {
          pes[a] ~= 1;
        }
      }
      long ans = 1;
      foreach (p, es; pes) {
        es.sort;
        es.reverse;
        const eSum = es[0 .. min(K, $)].sum;
        foreach (_; 0 .. eSum) {
          ans *= p;
          ans %= MO;
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}