import heapq from collections import defaultdict def main(): import sys input = sys.stdin.read data = input().split() idx = 0 N = int(data[idx]); idx +=1 M = int(data[idx]); idx +=1 P = int(data[idx]); idx +=1 A = list(map(int, data[idx:idx+N])) idx +=N # Preprocess A into B_i and m_i (A_i = B_i * P^m_i) B_list = [] m_list = [] for a in A: if a == 0: m = 0 B = 0 else: m = 0 tmp = a while tmp % P == 0: m +=1 tmp = tmp // P B = tmp B_list.append(B) m_list.append(m) heap = [] visited = defaultdict(lambda: float('inf')) initial_k = 1 initial_e = 0 initial_steps = 0 heapq.heappush(heap, (initial_steps, initial_k, initial_e)) visited[(initial_k, initial_e)] = initial_steps answer = -1 while heap: steps, k, e = heapq.heappop(heap) # Check if current steps is higher than recorded if steps > visited[(k, e)]: continue # Check division possibility if e > 0: # must divide new_e = e -1 new_k = k new_x = new_k * (P ** new_e) new_steps = steps +1 if new_x > M: answer = new_steps print(answer) return else: if new_steps < visited[(new_k, new_e)]: visited[(new_k, new_e)] = new_steps heapq.heappush(heap, (new_steps, new_k, new_e)) else: # e == 0: can multiply by any A_i for i in range(N): B_i = B_list[i] m_i = m_list[i] # Compute new_x after multiplying by B_i and P^m_i new_x_multiply = k * B_i * (P ** m_i) if new_x_multiply > M: current_candidate = steps +1 if answer == -1 or current_candidate < answer: answer = current_candidate print(answer) return continue else: new_k_after = k * B_i new_steps_after = steps + m_i +1 new_e_after = 0 if new_steps_after < visited.get((new_k_after, new_e_after), float('inf')): visited[(new_k_after, new_e_after)] = new_steps_after heapq.heappush(heap, (new_steps_after, new_k_after, new_e_after)) print(answer) if __name__ == '__main__': main()