Problem: Today Pari and Arya are playing a game called Remainders.

Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?

Note, that <image> means the remainder of x after dividing it by y.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 1 000 000) — the number of ancient integers and value k that is chosen by Pari.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 1 000 000).

Output

Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.

Examples

Input

4 5
2 3 5 12


Output

Yes


Input

2 7
2 3


Output

No

Note

In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.

In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.annotation.ElementType;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;


public class  Main{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastInput input = new FastInput(inputStream);
        FastOutput out = new FastOutput(outputStream);
        int n= input.scanInt();
        int k= input.scanInt();
        int a[]=new int [n];
        for(int i=0;i<n;i++){
            a[i]= input.scanInt();
        }
        int c[]=new int [200];
        c[0]=2;
        c[1]=3;
        c[2]=5;
        c[3]=7;
        int len=4;
        for(int i=10;i<=1000;i+=10){
            boolean is=true;
            for(int j=0;j<len;j++){
                if((i+1)%c[j]==0) {
                    is=false;
                    break;
                }
            }
            if(is){
                c[len++]=i+1;
            }
            is=true;
            for(int j=0;j<len;j++){
                if((i+3)%c[j]==0) {
                    is=false;
                    break;
                }
            }
            if(is){
                c[len++]=i+3;
            }
            is=true;
            for(int j=0;j<len;j++){
                if((i+7)%c[j]==0) {
                    is=false;
                    break;
                }
            }
            if(is){
                c[len++]=i+7;
            }
            is=true;
            for(int j=0;j<len;j++){
                if((i+9)%c[j]==0) {
                    is=false;
                    break;
                }
            }
            if(is){
                c[len++]=i+9;
            }
        }

        int b[][]=new int [100][2];
        int poi=0;
        for(int i=0;i<len;i++){
            if(k%c[i]==0){
                b[poi][0]=c[i];
                int time=0;
                for(;k%c[i]==0;){
                    time++;
                    k=k/c[i];
                }
                b[poi++][1]=time;
            }
        }

        if(k!=1){
            b[poi][0]=k;
            b[poi++][1]=1;
        }
        boolean eno[]=new boolean[poi];
        Arrays.sort(a);
        int x=0;
        for(int i=0;i<n;i++){
            if(a[i]!=x){
                x=a[i];
                for(int j=0;j<poi;j++){
                    if(!eno[j]){
                        int sum=0;
                        for(;b[j][1]!=0&&a[i]%b[j][0]==0;){
                            a[i]/=b[j][0];
                            sum++;
                        }
                        if(sum>=b[j][1]) eno[j]=true;
                        if(a[i]==1) break;
                    }
                }
            }
        }
        boolean ok=true;
        for(int i=0;i<poi;i++){
            if(!eno[i]) {
                ok=false;
                   }

        }
        if(ok){
            System.out.println("YES");
        }
        else{
            System.out.println("NO");
        }
        out.close();
    }
    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;
        public FastInput(InputStream is) {
            this.is = is;
        }
        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }
        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }
        public String next() {
            return readString();
        }
        public int scanInt() {
            int sign = 1;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }
            int val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            return (sign*val);
        }

        public String readString(StringBuilder builder) {
            skipBlank();
            while (next > 32) {
                builder.append((char) next);
                next = read();
            }
            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

    }
    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            return this;
        }
        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }
        public FastOutput println(int c) {
            return append(c).println();
        }
        public FastOutput println(String c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
//            flush();
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }
    }
}