package contest; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class Q980_2 { InputStream is; PrintWriter out; String INPUT = ""; int Z = 10000000; int[] lpf = enumLowestPrimeFactors(Z); void solve() { int[] primes = sieveEratosthenes(100000); long L = nl(), H = nl(); int[] mlpf = Arrays.copyOf(lpf, Z); for(int i = 0;i < mlpf.length;i++)mlpf[i] = -mlpf[i]; SegmentTreeRMQ st = new SegmentTreeRMQ(mlpf); out: for(int i = primes.length-1;i >= 0;i--){ int p = primes[i]; long q = H/p*p; while(q >= L && q != p){ if(q/p <= Z){ int ind = st.lastle((int)(q/p), -p); if(ind == -1)break; if((long)ind*p < L || ind == 1)break; out.println((long)ind*p); break out; } if(ok(q, p, primes)){ // found out.println(q); break out; }else{ q -= p; } } } } public static class SegmentTreeRMQ { public int M, H, N; public int[] st; public SegmentTreeRMQ(int n) { N = n; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new int[M]; Arrays.fill(st, 0, M, Integer.MAX_VALUE); } public SegmentTreeRMQ(int[] a) { N = a.length; M = Integer.highestOneBit(Math.max(N-1, 1))<<2; H = M>>>1; st = new int[M]; for(int i = 0;i < N;i++){ st[H+i] = a[i]; } Arrays.fill(st, H+N, M, Integer.MAX_VALUE); for(int i = H-1;i >= 1;i--)propagate(i); } public void update(int pos, int x) { st[H+pos] = x; for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i); } private void propagate(int i) { st[i] = Math.min(st[2*i], st[2*i+1]); } public int minx(int l, int r){ if(l >= r)return 0; int min = Integer.MAX_VALUE; while(l != 0){ int f = l&-l; if(l+f > r)break; int v = st[(H+l)/f]; if(v < min)min = v; l += f; } while(l < r){ int f = r&-r; int v = st[(H+r)/f-1]; if(v < min)min = v; r -= f; } return min; } public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);} private int min(int l, int r, int cl, int cr, int cur) { if(l <= cl && cr <= r){ return st[cur]; }else{ int mid = cl+cr>>>1; int ret = Integer.MAX_VALUE; if(cl < r && l < mid){ ret = Math.min(ret, min(l, r, cl, mid, 2*cur)); } if(mid < r && l < cr){ ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1)); } return ret; } } public int firstle(int l, int v) { int cur = H+l; while(true){ if(st[cur] <= v){ if(cur < H){ cur = 2*cur; }else{ return cur-H; } }else{ cur++; if((cur&cur-1) == 0)return -1; if((cur&1)==0)cur>>>=1; } } } public int lastle(int l, int v) { int cur = H+l; while(true){ if(st[cur] <= v){ if(cur < H){ cur = 2*cur+1; }else{ return cur-H; } }else{ if((cur&cur-1) == 0)return -1; cur--; if((cur&1)==1)cur>>>=1; } } } } boolean ok(long q, int p, int[] primes) { while(q % p == 0)q /= p; if(q == 1)return true; if(q < Z){ return lpf[(int)q] >= p; } for(int x : primes){ if(x == p)return true; if(q % x == 0)return false; } return true; } public static int[] enumLowestPrimeFactors(int n) { int tot = 0; int[] lpf = new int[n + 1]; int u = n + 32; double lu = Math.log(u); int[] primes = new int[(int) (u / lu + u / lu / lu * 1.5)]; for (int i = 2; i <= n; i++) lpf[i] = i; for (int p = 2; p <= n; p++) { if (lpf[p] == p) primes[tot++] = p; int tmp; for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) { lpf[tmp] = primes[i]; } } return lpf; } public static int[] sieveEratosthenes(int n) { if (n <= 32) { int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 }; for (int i = 0; i < primes.length; i++) { if (n < primes[i]) { return Arrays.copyOf(primes, i); } } return primes; } int u = n + 32; double lu = Math.log(u); int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)]; ret[0] = 2; int pos = 1; int[] isnp = new int[(n + 1) / 32 / 2 + 1]; int sup = (n + 1) / 32 / 2 + 1; int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 }; for (int tp : tprimes) { ret[pos++] = tp; int[] ptn = new int[tp]; for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31); for (int j = 0; j < sup; j += tp) { for (int i = 0; i < tp && i + j < sup; i++) { isnp[j + i] |= ptn[i]; } } } // 3,5,7 // 2x+3=n int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 }; int h = n / 2; for (int i = 0; i < sup; i++) { for (int j = ~isnp[i]; j != 0; j &= j - 1) { int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27]; int p = 2 * pp + 3; if (p > n) break; ret[pos++] = p; if ((long) p * p > n) continue; for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q; } } return Arrays.copyOf(ret, pos); } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); } public static void main(String[] args) throws Exception { new Q980_2().run(); } private byte[] inbuf = new byte[1024]; private int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }