import java.awt.Point; import java.io.*; import java.math.BigInteger; import java.nio.charset.*; import java.util.*; import java.util.function.*; class Main{ static boolean autoFlush = false; static SimpleScanner sc = new SimpleScanner(System.in); static SimpleWriter out = new SimpleWriter(System.out,autoFlush); public static void main(String[] args){ int N = sc.nextInt(); int K = sc.nextInt(); long[] A = sc.nextLong(N); HashMap map = new HashMap<>(); for(int i=0;i<=K;i++) map.put(A[i]+i,i); for(int i=1;i next = new HashMap<>(); for(Map.Entry entry:map.entrySet()){ long num = entry.getKey(); int count = entry.getValue(); for(int j=0;j+count<=K;j++) next.merge(MathFunction.gcd(A[i]+j,num),j+count,Integer::min); } map = next; } long ans = 1; for(long key:map.keySet()) ans = Math.max(ans,key); out.println(ans); out.close(); } } /*//////////////////////////// * My Library * @author viral *///////////////////////////// class Factorial{ long[] fact, inFact; long mod; Factorial(int N,long mod){ fact = new long[N+1]; fact[0] = fact[1] = 1; for(int i = 2;i<=N;++i) fact[i] = fact[i-1]*i%mod; inFact = new long[N+1]; inFact[N] = MathFunction.modPow(fact[N],mod-2,mod); for(int i = N;i>0;--i) inFact[i-1] = inFact[i]*i%mod; inFact[0] = 1; this.mod = mod; } long getFact(int num){ return fact[num]; } long getInFact(int num){ return inFact[num]; } long getInverse(int num){ return fact[num-1]*inFact[num]%mod; } long getCombi(int a,int b){ if(a E[][] rotateR(E[][] array,E[][] ans){ for(int i = 0;iarray[k][ans.length-index-1]); } return ans; } static long[][] rotateL(long[][] array){ long[][] ans = new long[array[0].length][array.length]; for(int i = 0;iarray[k][ans.length-index-1]); } return ans; } static char[][] rotateL(char[][] array){ char[][] ans = new char[array[0].length][array.length]; for(int i = 0;i E[][] rotateL(E[][] array,E[][] ans){ for(int i = 0;i> route){ int[] count = new int[route.size()]; int pathCount = 0; for(ArrayList path: route){ for(int point: path){ ++pathCount; ++count[point]; } } ArrayDeque deq = new ArrayDeque<>(); for(int i = 1;i0){ int nowP = deq.pollFirst(); for(int nextP: route.get(nowP)){ ans[index][0] = nowP; ans[index++][1] = nextP; if(--count[nextP]==0) deq.add(nextP); } } return ans; } static int[][] topologicalSort(int[][] route){ int[] count = new int[route.length]; int pathCount = 0; for(int[] path: route){ for(int point: path){ ++pathCount; ++count[point]; } } ArrayDeque deq = new ArrayDeque<>(); for(int i = 1;i0){ int nowP = deq.pollFirst(); for(int nextP: route[nowP]){ ans[index][0] = nowP; ans[index++][1] = nextP; if(--count[nextP]==0) deq.add(nextP); } } return ans; } static boolean nextPermutation(int[] array){ int index1 = 0; for(int i = 1;i> boolean nextPermutation(E[] array){ int index1 = 0; for(int i = 1;i=0;--i) sb.append(str.charAt(i)); return sb.toString(); } } class MathFunction{ static int[] numberForIntPrime = {2,7,61}; static long[] numberForLongPrime = {2,7,61,325,9375,28178,450775,9780504,1795265022}; static long gcd(long a,long b){ a = Math.abs(a); b = Math.abs(b); if(b==0) return a; long temp; while((temp = a%b)!=0){ a = b; b = temp; } return b; } static long lcm(long a,long b){ return a/gcd(a,b)*b; } static boolean isPrime(long n){ n = Math.abs(n); if(n==2L) return true; if(n==1L||(n&1L)==0L) return false; if(n<=4_759_123_141L) return isPrimeForInt(n); return isPrimeForBigInteger(n); } static boolean isPrimeForInt(long n){ long d = n-1; while((d&1)==0L) d >>= 1; for(long a: numberForIntPrime){ if(a>=n) return true; long t = d; long y = MathFunction.modPow(a,t,n); while(t>= 1; BigInteger bigN = BigInteger.valueOf(n); BigInteger bigNSubOne = bigN.subtract(BigInteger.ONE); BigInteger bigD = BigInteger.valueOf(d); for(long a: numberForLongPrime){ if(a>=n) return true; BigInteger t = bigD; BigInteger y = BigInteger.valueOf(a).modPow(t,bigN); while(t.compareTo(bigNSubOne)<0&&!y.equals(BigInteger.ONE)&&!y.equals(bigNSubOne)){ y = y.multiply(y).mod(bigN); t = t.shiftLeft(1); } if(!y.equals(bigNSubOne)&&(t.intValue()&1)==0) return false; } return true; } static int[] primes(int num){ if(num<2) return new int[0]; BitSet numbers = new BitSet(num+1); numbers.set(2,num+1); int limit = (int)Math.sqrt(num); for(int i=2;i<=limit;++i) if(numbers.get(i)) for(int j=i*i;j<=num;j+=i) if(numbers.get(j)) numbers.clear(j); int[] answer = new int[numbers.cardinality()]; int i = 2, index = 0; do{ i = numbers.nextSetBit(i); answer[index++] = i++; } while(index!=answer.length); return answer; } static long pow(long a,long b){ long ans = 1; while(b>0){ if((b&1)==1) ans *= a; a *= a; b >>= 1; } return ans; } static long modPow(long a,long b,long mod){ long ans = 1; a %= mod; while(b>0){ if((b&1)==1) ans *= a; ans %= mod; a *= a; a %= mod; b >>= 1; } return ans; } static long fact(int N){ long ans = 1; for(int i = 2;i<=N;++i) ans *= i; return ans; } static long modFact(int N,long mod){ long ans = 1; for(int i = 2;i<=N;++i){ ans *= i; ans %= mod; } return ans; } static long combi(long n,long r){ if(r<0||n> boolean rangeCheck(E num,E l,E r){ return 0<=l.compareTo(num)&&0> boolean rangeCheckOpen(E num,E l,E r){ return 0> boolean rangeCheckClose(E num,E l,E r){ return 0<=l.compareTo(num)&&0<=num.compareTo(r); } } class Searcher{ static int CYCLE_COUNT = Double.MAX_EXPONENT+53; static int downSearch(int[] array,int value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = c-1; else a = (ans=c)+1; } return ans; } static int downSearch(long[] array,long value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = c-1; else a = (ans=c)+1; } return ans; } static int downSearch(double[] array,double value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = c-1; else a = (ans=c)+1; } return ans; } static int downSearch(char[] array,int value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = c-1; else a = (ans=c)+1; } return ans; } static > int downSearch(E[] array,E value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c].compareTo(value)>0) b = c-1; else a = (ans=c)+1; } return ans; } static > int downSearch(List list,E value){ int a = 0,b = list.size()-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(list.get(c).compareTo(value)>0) b = c-1; else a = (ans=c)+1; } return ans; } static int downSearch(int a,int b,int value,IntUnaryOperator func){ int ans = a-1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsInt(c)>value) b = c-1; else a = (ans=c)+1; } return ans; } static long downSearch(long a,long b,long value,LongUnaryOperator func){ long ans = a-1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsLong(c)>value) b = c-1; else a = (ans=c)+1; } return ans; } static double search(double a,double b,double value,DoubleUnaryOperator func){ double ans = a-Math.abs(a),c; for(int $ = 0;$value) b = c; else a = (ans=c); } return ans; } static int upSearch(int[] array,int value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = (ans=c)-1; else a = c+1; } return ans; } static int upSearch(long[] array,long value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = (ans=c)-1; else a = c+1; } return ans; } static int upSearch(double[] array,double value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = (ans=c)-1; else a = c+1; } return ans; } static int upSearch(char[] array,char value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = (ans=c)-1; else a = c+1; } return ans; } static > int upSearch(E[] array,E value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c].compareTo(value)>=0) b = (ans=c)-1; else a = c+1; } return ans; } static > int upSearch(List list,E value){ int a = 0,b = list.size()-1,ans = list.size(),c; while(a-b<1){ c = (a+b)/2; if(list.get(c).compareTo(value)>=0) b = (ans=c)-1; else a = c+1; } return ans; } static int upSearch(int a,int b,int value,IntUnaryOperator func){ int ans = b+1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsInt(c)>=value) b = (ans=c)-1; else a = c+1; } return ans; } static long upSearch(long a,long b,long value,LongUnaryOperator func){ long ans = b+1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsLong(c)>=value) b = (ans=c)-1; else a = c+1; } return ans; } static int underSearch(int[] array,int value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = c-1; else a = (ans=c)+1; } return ans; } static int underSearch(long[] array,long value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = c-1; else a = (ans=c)+1; } return ans; } static int underSearch(double[] array,double value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = c-1; else a = (ans=c)+1; } return ans; } static int underSearch(char[] array,char value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c]>=value) b = c-1; else a = (ans=c)+1; } return ans; } static > int underSearch(E[] array,E value){ int a = 0,b = array.length-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(array[c].compareTo(value)>=0) b = c-1; else a = (ans=c)+1; } return ans; } static > int underSearch(List list,E value){ int a = 0,b = list.size()-1,ans = -1,c; while(a-b<1){ c = (a+b)/2; if(list.get(c).compareTo(value)>=0) b = c-1; else a = (ans=c)+1; } return ans; } static int underSearch(int a,int b,int value,IntUnaryOperator func){ int ans = a-1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsInt(c)>=value) b = c-1; else a = (ans=c)+1; } return ans; } static long underSearch(long a,long b,long value,LongUnaryOperator func){ long ans = a-1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsLong(c)>=value) b = c-1; else a = (ans=c)+1; } return ans; } static int overSearch(int[] array,int value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = (ans=c)-1; else a = c+1; } return ans; } static int overSearch(long[] array,long value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = (ans=c)-1; else a = c+1; } return ans; } static int overSearch(double[] array,double value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = (ans=c)-1; else a = c+1; } return ans; } static int overSearch(char[] array,char value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c]>value) b = (ans=c)-1; else a = c+1; } return ans; } static > int overSearch(E[] array,E value){ int a = 0,b = array.length-1,ans = array.length,c; while(a-b<1){ c = (a+b)/2; if(array[c].compareTo(value)>0) b = (ans=c)-1; else a = c+1; } return ans; } static > int overSearch(List list,E value){ int a = 0,b = list.size()-1,ans = list.size(),c; while(a-b<1){ c = (a+b)/2; if(list.get(c).compareTo(value)>0) b = (ans=c)-1; else a = c+1; } return ans; } static int overSearch(int a,int b,int value,IntUnaryOperator func){ int ans = b+1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsInt(c)>value) b = (ans=c)-1; else a = c+1; } return ans; } static long overSearch(long a,long b,long value,LongUnaryOperator func){ long ans = b+1,c; while(a-b<1){ c = (a+b)/2; if(func.applyAsLong(c)>value) b = (ans=c)-1; else a = c+1; } return ans; } } class BIT{ int size; long[] tree; BIT(int n){ size = n; tree = new long[n+1]; } long sum(int i){ long sum = 0; while(i>0){ sum += tree[i]; i ^= i&(-i); } return sum; } void add(int i,long x){ while(i<=size){ tree[i] += x; i += i&(-i); } } void clear(){ Arrays.fill(tree,0L); } } class RollingHash implements Comparable{ static long BASE = new Random().nextInt(1000)+Character.MAX_VALUE+1; static long MASK30 = (1L<<30)-1; static long MASK31 = (1L<<31)-1; static long MOD = (1L<<61)-1; static long MASK61 = MOD; long[] hash; String string; RollingHash(String str){ string = str; hash = new long[str.length()+1]; roll(); } void roll(){ int len = string.length(); for(int i = 1;i<=len;++i){ hash[i] = multiply(hash[i-1],BASE)+string.charAt(i-1)-' '+1; if(MOD<=hash[i]) hash[i] -= MOD; } } static long multiply(long a,long b){ long au = a>>31; long ad = a&MASK31; long bu = b>>31; long bd = b&MASK31; long mid = ad*bu+au*bd; long midu = mid>>30; long midd = mid&MASK30; return mod(au*bu*2+midu+(midd<<31)+ad*bd); } static long mod(long x){ long xu = x>>61; long xd = x&MASK61; long ans = xu+xd; if(MOD<=ans) ans -= MOD; return ans; } long getHash(int l,int r){ return (hash[r]-multiply(hash[l],modBasePow(r-l))+MOD)%MOD; } static long modBasePow(long b){ long ans = 1; long a = BASE; while(b>0){ if((b&1)==1) ans = multiply(ans,a); a = multiply(a,a); b >>= 1; } return ans; } boolean equals(RollingHash rh,int l1,int r1,int l2,int r2){ if(r1-l1!=r2-l2) return false; return getHash(l1,r1)==rh.getHash(l2,r2); } int length(){ return string.length(); } public int hashCode(){ return string.hashCode(); } public String toString(){ return string; } public boolean equals(Object o){ if(o instanceof RollingHash rh) return equals(rh,0,length(),0,rh.length()); return false; } public int compareTo(RollingHash rh){ return string.compareTo(rh.toString()); } int compareTo(String str){ return string.compareTo(str); } char charAt(int i){ return string.charAt(i); } int compareToIgnoreCase(RollingHash rh){ return string.compareToIgnoreCase(rh.toString()); } int compareToIgnoreCase(String str){ return string.compareToIgnoreCase(str); } void concat(RollingHash rh){ concat(rh.toString()); } void concat(String str){ string = string.concat(str); hash = new long[string.length()+1]; roll(); } boolean contains(RollingHash rh){ long hash = rh.getHash(0,rh.length()); int len = length()-rh.length(); for(int i = 0;i<=len;++i) if(hash==getHash(i,rh.length()+i)) return true; return false; } boolean contains(String str){ return indexOf(str)!=-1; } int indexOf(int ch){ return indexOf(ch,0); } int indexOf(int ch,int fromIndex){ int len = length(); for(int i = fromIndex;i=0;--i) if(string.charAt(i)==ch) return i; return -1; } int lastIndexOf(int ch){ return lastIndexOf(ch,length()-1); } } @SuppressWarnings("unchecked") abstract class SegmentTree{ int N, size; E def; Object[] node; SegmentTree(int n,E def,boolean include){ int num = 2; while(num>1-(include?1:0); node = new Object[N]; this.def = def; Arrays.fill(node,this.def); } SegmentTree(E[] arr,E def,boolean include){ int num = 2; while(num>1-(include?1:0); node = new Object[N]; this.def = def; System.arraycopy(arr,0,node,N>>1,arr.length); for(int i = arr.length+(N>>1);i>1)-1;i>0;i--) node[i] = function((E)node[i<<1],(E)node[(i<<1)+1]); } void update(int n,E value){ n += size; node[n] = value; n >>= 1; while(n>0){ node[n] = function((E)node[n<<1],(E)node[(n<<1)+1]); n >>= 1; } } E get(int a){ return (E)node[a+size]; } E answer(){ return (E)node[1]; } E query(int l,int r){ l += size; r += size; E answer = def; while(l>0&&r>0&&l<=r){ if(l%2==1) answer = function((E)node[l++],answer); l >>= 1; if(r%2==0) answer = function(answer,(E)node[r--]); r >>= 1; } return answer; } abstract E function(E a,E b); } class UnionFind{ int[] par, rank, size, path; int count; UnionFind(int N){ count = N; par = new int[N]; rank = new int[N]; size = new int[N]; path = new int[N]; Arrays.fill(par,-1); Arrays.fill(size,1); } int root(int ind){ if(par[ind]==-1) return ind; else return par[ind] = root(par[ind]); } boolean isSame(int x,int y){ return root(x)==root(y); } boolean unite(int x,int y){ int rx = root(x); int ry = root(y); ++path[rx]; if(rx==ry) return false; if(rank[rx]' '){ ans.append((char)c); c = read(); } return ans.toString(); } BigInteger nextBigInteger(){ return new BigInteger(next()); } byte[] nextByte(int n){ byte[] ans = new byte[n]; for(int i = 0;i0){ out.write(buf,0,count); count = 0; } } public void write(int b) throws IOException{ if(count>=buf.length) flushBuffer(); buf[count++] = (byte)b; } public void write(byte[] b,int off,int len) throws IOException{ if(len>=buf.length){ flushBuffer(); out.write(b,off,len); return; } if(len>buf.length-count) flushBuffer(); System.arraycopy(b,off,buf,count,len); count += len; } public void flush() throws IOException{ flushBuffer(); out.flush(); } } class SimpleWriter implements Appendable, Closeable, Flushable, AutoCloseable{ Writer out; boolean autoFlush; boolean trouble = false; Formatter formatter; PrintStream psOut = null; static Charset toCharset(String csn){ if(csn==null) throw new NullPointerException("charsetName"); try{ return Charset.forName(csn); }catch(IllegalCharsetNameException|UnsupportedCharsetException e){ e.printStackTrace(); System.exit(1); return null; } } SimpleWriter(Writer out){ this(out,false); } SimpleWriter(Writer out,boolean autoFlush){ this.out = out; this.autoFlush = autoFlush; } SimpleWriter(OutputStream out){ this(out,false); } SimpleWriter(OutputStream out,boolean autoFlush){ this(out,autoFlush,Charset.defaultCharset()); } SimpleWriter(OutputStream out,boolean autoFlush,Charset charset){ this(new BufferedWriter(new OutputStreamWriter(new SimpleOutputStream(out),charset)),autoFlush); if(out instanceof PrintStream) psOut = (PrintStream)out; } void ensureOpen() throws IOException{ if(out==null) throw new IOException("Stream closed"); } public void flush(){ try{ ensureOpen(); out.flush(); }catch(IOException x){ trouble = true; } } public void close(){ try{ if(out==null) return; out.close(); out = null; }catch(IOException x){ trouble = true; } } boolean checkError(){ if(out!=null) flush(); else if(psOut!=null) return psOut.checkError(); return trouble; } void setError(){ trouble = true; } void clearError(){ trouble = false; } void write(int c){ try{ ensureOpen(); out.write(c); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } } void write(char[] buf,int off,int len){ try{ ensureOpen(); out.write(buf,off,len); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } } void write(char[] buf){ write(buf,0,buf.length); } void write(String s,int off,int len){ try{ ensureOpen(); out.write(s,off,len); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } } void write(String s){ write(s,0,s.length()); } void newLine(){ try{ ensureOpen(); out.write(System.lineSeparator()); if(autoFlush) out.flush(); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } } void print(boolean b){ write(b?"true":"false"); } void print(char c){ write(c); } void print(int i){ write(String.valueOf(i)); } void print(long l){ write(String.valueOf(l)); } void print(float f){ write(String.valueOf(f)); } void print(double d){ write(String.valueOf(d)); } void print(char[] s){ write(s); } void print(String s){ write(s); } void print(Object obj){ write(obj.toString()); } void println(){ newLine(); } void println(boolean x){ print(x); println(); } void println(char x){ print(x); println(); } void println(int x){ print(x); println(); } void println(long x){ print(x); println(); } void println(float x){ print(x); println(); } void println(double x){ print(x); println(); } void println(char[] x){ print(x); println(); } void println(String x){ print(x); println(); } void println(Object x){ print(x.toString()); println(); } SimpleWriter printf(String format,Object... args){ return format(format,args); } SimpleWriter printf(Locale l,String format,Object... args){ return format(l,format,args); } SimpleWriter format(String format,Object... args){ try{ ensureOpen(); if((formatter==null)||(formatter.locale()!=Locale.getDefault())) formatter = new Formatter(this); formatter.format(Locale.getDefault(),format,args); if(autoFlush) out.flush(); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } return this; } SimpleWriter format(Locale l,String format,Object... args){ try{ ensureOpen(); if((formatter==null)||(formatter.locale()!=l)) formatter = new Formatter(this,l); formatter.format(l,format,args); if(autoFlush) out.flush(); }catch(InterruptedIOException x){ Thread.currentThread().interrupt(); }catch(IOException x){ trouble = true; } return this; } public SimpleWriter append(CharSequence csq){ write(String.valueOf(csq)); return this; } public SimpleWriter append(CharSequence csq,int start,int end){ if(csq==null) csq = "null"; return append(csq.subSequence(start,end)); } public SimpleWriter append(char c){ write(c); return this; } void println(int[] array){ println(array,' '); } void println(int[] array,String str){ print(array[0]); for(int i = 1;i void println(E[] array){ println(array,' '); } void println(E[] array,String str){ print(array[0]); for(int i = 1;i void println(E[] array,char c){ print(array[0]); for(int i = 1;i void println(E[][] arrays){ println(arrays,' '); } void println(E[][] arrays,String str){ for(E[] array: arrays) println(array,str); } void println(E[][] arrays,char c){ for(E[] array: arrays) println(array,c); } void println(List list){ println(list,' '); } void println(List list,String str){ if(list.size()==0){ println(); return; } print(list.get(0)); for(int i = 1;i void println(List list,char c){ if(list.size()==0){ println(); return; } print(list.get(0)); for(int i = 1;i