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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool isPrime(int n) {
  if (n < 2) {
    return 0;
  }
  if (n % 2 == 0) {
    return n == 2;
  }
  for (int i = 3; i * i <= n; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
int gcd(int a, int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long ncr(int n, int r) {
  if (n < r) return 0;
  if (r == 0) return 1;
  return n * ncr(n - 1, r - 1) / r;
}
class DSU {
  int setsCount;
  vector<int> siz;
  mutable vector<int> par;

 public:
  DSU(int n) {
    setsCount = n;
    siz.resize(n, 1);
    par.resize(n);
    iota(par.begin(), par.end(), 0);
  }
  int findSetId(int u) const {
    return u == par[u] ? u : par[u] = findSetId(par[u]);
  }
  bool areInSameSet(int u, int v) const { return findSetId(u) == findSetId(v); }
  bool unionSets(int u, int v) {
    u = findSetId(u);
    v = findSetId(v);
    if (u == v) {
      return false;
    }
    setsCount--;
    siz[v] += siz[u];
    par[u] = v;
    return true;
  }
  int getSetSize(int u) const { return siz[findSetId(u)]; }
  int getSetsCount() const { return setsCount; }
};
struct edge {
  int from, to;
  int cost;
  bool operator<(const edge &t) const { return cost < t.cost; }
};
const long double pi = 3.141592653589793238462643383279502884;
string toBinary(int n) {
  string s = "";
  while (n > 0) {
    if (n % 2 == 0)
      s += "0";
    else
      s += "1";
    n /= 2;
  }
  reverse(s.begin(), s.end());
  return s;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    if (n % 2 != 0 && k % 2 == 0)
      cout << "NO"
           << "\n";
    else {
      int x = 0;
      if (n % 2 == 0) {
        if (k % 2 != 0) {
          if (2 * (k - 1) >= n)
            cout << "NO"
                 << "\n";
          else {
            cout << "YES"
                 << "\n";
            for (int i = 0; i < k - 1; i++) cout << 2 << " ";
            cout << n - 2 * (k - 1) << "\n";
          }
        } else {
          if ((k - 1) >= n)
            cout << "NO"
                 << "\n";
          else {
            cout << "YES"
                 << "\n";
            for (int i = 0; i < k - 1; i++) cout << 1 << " ";
            cout << n - (k - 1) << "\n";
          }
        }
      } else {
        if ((k - 1) >= n)
          cout << "NO"
               << "\n";
        else {
          cout << "YES"
               << "\n";
          for (int i = 0; i < k - 1; i++) cout << 1 << " ";
          cout << n - (k - 1) << "\n";
        }
      }
    }
  }
  return 0;
}