Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in JAVA):

Solution:
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.math.BigDecimal;
    import java.math.RoundingMode;
    import java.util.*;

    import javax.lang.model.type.IntersectionType;
    import javax.swing.text.html.CSS;
    public class codeforces {
        public static void main(String[] args) {
            PrintWriter out = new PrintWriter(System.out);
            InputReader sc = new InputReader(System.in);
            int t=sc.nextInt();
            while(t-->0) {
                long n = sc.nextLong();
                long k = sc.nextLong();
                long one=n-(k-1);
                long two=n-(k-1)*2;
                if(n%k==0)
                {
                    System.out.println("YES");
                    for(int i=0;i<k;i++)
                        System.out.print(n/k+" ");
                    System.out.println();
                }
                else if(one%2==1)
                {
                    System.out.println("YES");
                    for(int i=1;i<=k-1;i++)
                        System.out.print(1+" ");
                    System.out.println(one);
                }
                else if(two%2==0 && two>0)
                {
                    System.out.println("YES");
                    for(int i=1;i<=k-1;i++)
                        System.out.print(2+" ");
                    System.out.println(two);
                }
                else
                    System.out.println("NO");
            }

        }





        static class InputReader {
            private InputStream in;
            private byte[] buffer = new byte[1024];
            private int curbuf;
            private int lenbuf;
            public InputReader(InputStream in) {
                this.in = in;
                this.curbuf = this.lenbuf = 0;
            }
            public boolean hasNextByte() {
                if (curbuf >= lenbuf) {
                    curbuf = 0;
                    try {
                        lenbuf = in.read(buffer);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (lenbuf <= 0)
                        return false;
                }
                return true;
            }

            private int readByte() {
                if (hasNextByte())
                    return buffer[curbuf++];
                else
                    return -1;
            }

            private boolean isSpaceChar(int c) {
                return !(c >= 33 && c <= 126);
            }

            private void skip() {
                while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                    curbuf++;
            }

            public boolean hasNext() {
                skip();
                return hasNextByte();
            }

            public String next() {
                if (!hasNext())
                    throw new NoSuchElementException();
                StringBuilder sb = new StringBuilder();
                int b = readByte();
                while (!isSpaceChar(b)) {
                    sb.appendCodePoint(b);
                    b = readByte();
                }
                return sb.toString();
            }

            public int nextInt() {
                if (!hasNext())
                    throw new NoSuchElementException();
                int c = readByte();
                while (isSpaceChar(c))
                    c = readByte();
                boolean minus = false;
                if (c == '-') {
                    minus = true;
                    c = readByte();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res = res * 10 + c - '0';
                    c = readByte();
                } while (!isSpaceChar(c));
                return (minus) ? -res : res;
            }

            public long nextLong() {
                if (!hasNext())
                    throw new NoSuchElementException();
                int c = readByte();
                while (isSpaceChar(c))
                    c = readByte();
                boolean minus = false;
                if (c == '-') {
                    minus = true;
                    c = readByte();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res = res * 10 + c - '0';
                    c = readByte();
                } while (!isSpaceChar(c));
                return (minus) ? -res : res;
            }

            public double nextDouble() {
                return Double.parseDouble(next());
            }

            public int[] nextIntArray(int n) {
                int[] a = new int[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextInt();
                return a;
            }

            public long[] nextLongArray(int n) {
                long[] a = new long[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextLong();
                return a;
            }

            public char[][] nextCharMap(int n, int m) {
                char[][] map = new char[n][m];
                for (int i = 0; i < n; i++)
                    map[i] = next().toCharArray();
                return map;
            }
        }
    }
    class SegTree<S> {
        final int MAX;

        final int N;
        final java.util.function.BinaryOperator<S> op;
        final S E;

        final S[] data;

        @SuppressWarnings("unchecked")
        public SegTree(int n, java.util.function.BinaryOperator<S> op, S e) {
            this.MAX = n;
            int k = 1;
            while (k < n) k <<= 1;
            this.N = k;
            this.E = e;
            this.op = op;
            this.data = (S[]) new Object[N << 1];
            java.util.Arrays.fill(data, E);
        }

        public SegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e) {
            this(dat.length, op, e);
            build(dat);
        }

        private void build(S[] dat) {
            int l = dat.length;
            System.arraycopy(dat, 0, data, N, l);
            for (int i = N - 1; i > 0; i--) {
                data[i] = op.apply(data[i << 1 | 0], data[i << 1 | 1]);
            }
        }

        public void set(int p, S x) {
            exclusiveRangeCheck(p);
            data[p += N] = x;
            p >>= 1;
            while (p > 0) {
                data[p] = op.apply(data[p << 1 | 0], data[p << 1 | 1]);
                p >>= 1;
            }
        }

        public S get(int p) {
            exclusiveRangeCheck(p);
            return data[p + N];
        }

        public S prod(int l, int r) {
            if (l > r) {
                throw new IllegalArgumentException(
                        String.format("Invalid range: [%d, %d)", l, r)
                );
            }
            inclusiveRangeCheck(l);
            inclusiveRangeCheck(r);
            S sumLeft = E;
            S sumRight = E;
            l += N; r += N;
            while (l < r) {
                if ((l & 1) == 1) sumLeft = op.apply(sumLeft, data[l++]);
                if ((r & 1) == 1) sumRight = op.apply(data[--r], sumRight);
                l >>= 1; r >>= 1;
            }
            return op.apply(sumLeft, sumRight);
        }

        public S allProd() {
            return data[1];
        }

        public int maxRight(int l, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(l);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (l == MAX) return MAX;
            l += N;
            S sum = E;
            do {
                l >>= Integer.numberOfTrailingZeros(l);
                if (!f.test(op.apply(sum, data[l]))) {
                    while (l < N) {
                        l = l << 1;
                        if (f.test(op.apply(sum, data[l]))) {
                            sum = op.apply(sum, data[l]);
                            l++;
                        }
                    }
                    return l - N;
                }
                sum = op.apply(sum, data[l]);
                l++;
            } while ((l & -l) != l);
            return MAX;
        }

        public int minLeft(int r, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(r);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (r == 0) return 0;
            r += N;
            S sum = E;
            do {
                r--;
                while (r > 1 && (r & 1) == 1) r >>= 1;
                if (!f.test(op.apply(data[r], sum))) {
                    while (r < N) {
                        r = r << 1 | 1;
                        if (f.test(op.apply(data[r], sum))) {
                            sum = op.apply(data[r], sum);
                            r--;
                        }
                    }
                    return r + 1 - N;
                }
                sum = op.apply(data[r], sum);
            } while ((r & -r) != r);
            return 0;
        }

        private void exclusiveRangeCheck(int p) {
            if (p < 0 || p >= MAX) {
                throw new IndexOutOfBoundsException(
                        String.format("Index %d out of bounds for the range [%d, %d).", p, 0, MAX)
                );
            }
        }

        private void inclusiveRangeCheck(int p) {
            if (p < 0 || p > MAX) {
                throw new IndexOutOfBoundsException(
                        String.format("Index %d out of bounds for the range [%d, %d].", p, 0, MAX)
                );
            }
        }
    }
    class MathLib{
        static int LowerBound(int a[], int x) { // x is the target value or key
            int l=-1,r=a.length;
            while(l+1<r) {
                int m=(l+r)>>>1;
                if(a[m]>=x) r=m;
                else l=m;
            }
            return r;
        }
        static int UpperBound(int a[], int x) {// x is the key or target value
            int l=-1,r=a.length;
            while(l+1<r) {
                int m=(l+r)>>>1;
                if(a[m]<=x) l=m;
                else r=m;
            }
            return l+1;
        }
        private static long safe_mod(long x, long m){
            x %= m;
            if(x<0) x += m;
            return x;
        }

        private static long[] inv_gcd(long a, long b){
            a = safe_mod(a, b);
            if(a==0) return new long[]{b,0};

            long s=b, t=a;
            long m0=0, m1=1;
            while(t>0){
                long u = s/t;
                s -= t*u;
                m0 -= m1*u;
                long tmp = s; s = t; t = tmp;
                tmp = m0; m0 = m1; m1 = tmp;
            }
            if(m0<0) m0 += b/s;
            return new long[]{s,m0};
        }

        public static long gcd(long a, long b){
            a = java.lang.Math.abs(a);
            b = java.lang.Math.abs(b);
            return inv_gcd(a, b)[0];
        }
        public static long lcm(long a, long b){
            a = java.lang.Math.abs(a);
            b = java.lang.Math.abs(b);
            return a / gcd(a,b) * b;
        }

        public static long pow_mod(long x, long n, int m){
            assert n >= 0;
            assert m >= 1;
            if(m == 1)return 0L;
            x = safe_mod(x, m);
            long ans = 1L;
            while(n > 0){
                if((n&1) == 1) ans = (ans * x) % m;
                x = (x*x) % m;
                n >>>= 1;
            }
            return ans;
        }

        public static long[] crt(long[] r, long[] m){
            assert(r.length == m.length);
            int n = r.length;

            long r0=0, m0=1;
            for(int i=0; i<n; i++){
                assert(1 <= m[i]);
                long r1 = safe_mod(r[i], m[i]), m1 = m[i];
                if(m0 < m1){
                    long tmp = r0; r0 = r1; r1 = tmp;
                    tmp = m0; m0 = m1; m1 = tmp;
                }
                if(m0%m1 == 0){
                    if(r0%m1 != r1) return new long[]{0,0};
                    continue;
                }

                long[] ig = inv_gcd(m0, m1);
                long g = ig[0], im = ig[1];

                long u1 = m1/g;
                if((r1-r0)%g != 0) return new long[]{0,0};

                long x = (r1-r0) / g % u1 * im % u1;

                r0 += x * m0;
                m0 *= u1;
                if(r0<0) r0 += m0;
                //System.err.printf("%d %d\n", r0, m0);
            }
            return new long[]{r0, m0};
        }
        public static long floor_sum(long n, long m, long a, long b){
            long ans = 0;
            if(a >= m){
                ans += (n-1) * n * (a/m) / 2;
                a %= m;
            }
            if(b >= m){
                ans += n * (b/m);
                b %= m;
            }

            long y_max = (a*n+b) / m;
            long x_max = y_max * m - b;
            if(y_max == 0) return ans;
            ans += (n - (x_max+a-1)/a) * y_max;
            ans += floor_sum(y_max, a, m, (a-x_max%a)%a);
            return ans;
        }

        public static java.util.ArrayList<Long> divisors(long n){
            java.util.ArrayList<Long> divisors = new ArrayList<>();
            java.util.ArrayList<Long> large = new ArrayList<>();

            for(long i=1; i*i<=n; i++) if(n%i==0){
                divisors.add(i);
                if(i*i<n) large.add(n/i);
            }
            for(int p=large.size()-1; p>=0; p--){
                divisors.add(large.get(p));
            }
            return divisors;
        }
    }