from math import gcd def MillerRabin(n): if n <= 1: return False elif n == 2: return True elif n % 2 == 0: return False if n < 4759123141: A = [2, 7, 61] else: A = [2, 325, 9375, 28178, 450775, 9780504, 1795265022] s = 0 d = n - 1 while d % 2 == 0: s += 1 d >>= 1 for a in A: if a % n == 0: return True x = pow(a, d, n) if x != 1: for t in range(s): if x == n - 1: break x = x * x % n else: return False return True def pollard(n): # https://qiita.com/t_fuki/items/7cd50de54d3c5d063b4a if n % 2 == 0: return 2 m = int(n**0.125) + 1 step = 0 while 1: step += 1 def f(x): return (x * x + step) % n y = k = 0 g = q = r = 1 while g == 1: x = y while k < 3 * r // 4: y = f(y) k += 1 while k < r and g == 1: ys = y for _ in range(min(m, r - k)): y = f(y) q = q * abs(x - y) % n g = gcd(q, n) k += m k = r r <<= 1 if g == n: g = 1 y = ys while g == 1: y = f(y) g = gcd(abs(x - y), n) if g == n: continue if MillerRabin(g): return g elif MillerRabin(n // g): return n // g else: return pollard(g) def primefact(n): res = [] while n > 1 and not MillerRabin(n): p = pollard(n) while n % p == 0: res.append(p) n //= p if n != 1: res.append(n) return sorted(res) def primedict(n): P = primefact(n) ret = {} for p in P: ret[p] = ret.get(p, 0) + 1 return ret n, a, b, c = map(int, input().split()) x = 1 fact = [1, 1] m = 400200 while fact[-1] < m: x += 1 fact.append(fact[-1] * x) if m % n == 0: m += 1 inf = 1 << 60 dist = [inf] * (m + 2) dist[2] = a for i in range(2, m + 1): dist[i + 1] = min(dist[i + 1], dist[i] + a) if i < x: dist[fact[i]] = min(dist[fact[i]], dist[i] + c) else: dist[m + 1] = min(dist[m + 1], dist[i] + c) cost = b nex = i while nex * i <= m: nex *= i cost *= b dist[nex] = min(dist[nex], dist[i] + cost) cost *= b dist[m + 1] = min(dist[m + 1], dist[i] + cost) ans = 1 << 60 for i in range(n, m + 2, n): ans = min(ans, dist[i]) ps = primedict(n) def ok(x): for k, v in ps.items(): tot = 0 y = x while y > 0: y //= k tot += y if tot >= v: break if tot < v: return False return True l = 1 r = n while r - l > 1: mid = (l + r) // 2 if ok(mid): r = mid else: l = mid ans = min(ans, min(dist[r:]) + c) print(ans)