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;
long long pow_mod(long long nn, long long pp, long long mm) {
  long long res = 1;
  while (pp > 0) {
    if (pp & 1) res = (res * nn) % mm;
    pp = pp >> 1;
    nn = (nn * nn) % mm;
  }
  return res;
}
class stdout_cus {
  short float_prec = 7;

 public:
  inline stdout_cus operator<<(const int& arg) {
    printf("%d", arg);
    return *this;
  }
  inline stdout_cus operator<<(const short& arg) {
    printf("%d", arg);
    return *this;
  }
  inline stdout_cus operator<<(const bool& arg) {
    printf("%d", arg);
    return *this;
  }
  inline stdout_cus operator<<(const unsigned int& arg) {
    printf("%u", arg);
    return *this;
  }
  inline stdout_cus operator<<(const unsigned short& arg) {
    printf("%u", arg);
    return *this;
  }
  inline stdout_cus operator<<(const long long& arg) {
    printf("%lld", arg);
    return *this;
  }
  inline stdout_cus operator<<(const unsigned long long& arg) {
    printf("%llu", arg);
    return *this;
  }
  inline stdout_cus operator<<(const double& arg) {
    printf("%.*f", float_prec, arg);
    return *this;
  }
  inline stdout_cus operator<<(const float& arg) {
    printf("%.*f", float_prec, arg);
    return *this;
  }
  inline stdout_cus operator<<(const char& arg) {
    printf("%c", arg);
    return *this;
  }
  inline stdout_cus operator<<(const unsigned char& arg) {
    printf("%c", arg);
    return *this;
  }
  inline stdout_cus operator<<(const char* arg) {
    printf("%s", arg);
    return *this;
  }
  inline stdout_cus operator<<(const std::string& arg) {
    printf("%s", arg.c_str());
    return *this;
  }
  inline stdout_cus operator<<(const stdout_cus&) { return *this; }
  inline void ignore() { fflush(stdout); }
  inline stdout_cus precision(short prec) {
    float_prec = prec;
    return *this;
  }
} cout_cus;
class stdin_cus {
 public:
  inline stdin_cus operator>>(const int& arg) {
    scanf(" %d", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const short& arg) {
    scanf(" %d", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const bool& arg) {
    scanf(" %d", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const unsigned int& arg) {
    scanf(" %u", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const unsigned short& arg) {
    scanf(" %u", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const long long& arg) {
    scanf(" %lld", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const unsigned long long& arg) {
    scanf(" %llu", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const double& arg) {
    scanf(" %lf", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const float& arg) {
    scanf(" %f", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const char& arg) {
    scanf(" %c", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const unsigned char& arg) {
    scanf(" %c", &arg);
    return *this;
  }
  inline stdin_cus operator>>(const char* arg) {
    scanf(" %s", arg);
    return *this;
  }
  inline stdin_cus operator>>(std::string& arg) {
    char tmp[1000000];
    scanf(" %s", tmp);
    arg = tmp;
    return *this;
  }
  inline void ignore() { fflush(stdin); }
} cin_cus;
void olium();
int main() {
  0;
  int t = 1;
  cin_cus >> t;
  for (long long i = 1; i <= t; i++) {
    olium();
  }
  return 0;
}
void olium() {
  long long n, k;
  cin_cus >> n >> k;
  if ((n - (2 * (k - 1))) % 2 == 0 && (n - (2 * (k - 1))) > 0) {
    cout_cus << "YES\n";
    cout_cus << (n - (2 * (k - 1))) << ' ';
    k--;
    while (k--) {
      cout_cus << 2 << ' ';
    }
    cout_cus << '\n';
  } else if ((n - (k - 1)) % 2 == 1) {
    cout_cus << "YES\n";
    cout_cus << (n - (k - 1)) << ' ';
    k--;
    while (k--) {
      cout_cus << 1 << ' ';
    }
    cout_cus << '\n';
  } else {
    cout_cus << "NO\n";
  }
}