Problem: Phoenix has n blocks of height h_1, h_2, ..., h_n, and all h_i don't exceed some value x. He plans to stack all n blocks into m separate towers. The height of a tower is simply the sum of the heights of its blocks. For the towers to look beautiful, no two towers may have a height difference of strictly more than x. 

Please help Phoenix build m towers that look beautiful. Each tower must have at least one block and all blocks must be used.

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains three integers n, m, and x (1 ≤ m ≤ n ≤ 10^5; 1 ≤ x ≤ 10^4) — the number of blocks, the number of towers to build, and the maximum acceptable height difference of any two towers, respectively. 

The second line of each test case contains n space-separated integers (1 ≤ h_i ≤ x) — the heights of the blocks. 

It is guaranteed that the sum of n over all the test cases will not exceed 10^5.

Output

For each test case, if Phoenix cannot build m towers that look beautiful, print NO. Otherwise, print YES, followed by n integers y_1, y_2, ..., y_n, where y_i (1 ≤ y_i ≤ m) is the index of the tower that the i-th block is placed in.

If there are multiple solutions, print any of them.

Example

Input


2
5 2 3
1 2 3 1 2
4 3 3
1 1 2 3


Output


YES
1 1 1 2 2
YES
1 2 2 3

Note

In the first test case, the first tower has height 1+2+3=6 and the second tower has height 1+2=3. Their difference is 6-3=3 which doesn't exceed x=3, so the towers are beautiful.

In the second test case, the first tower has height 1, the second tower has height 1+2=3, and the third tower has height 3. The maximum height difference of any two towers is 3-1=2 which doesn't exceed x=3, so the towers are beautiful.

Solution (in CPP):

Solution:

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define PI 3.14159265
#define pb push_back
#define en cout<<'\n'
#define vec vector<ll>
#define vecs vector<string>
#define pii pair<ll,ll>
#define VP vector< pii >
#define setbits(x)  __builtin_popcountll(x)
#define zrobits(x)  __builtin_ctzll(x)
#define all(v) (v).begin(),(v).end()
#define ff first
#define ss second
#define mm " "
#define MM " "
#define mll map<ll,ll>
#define f(i,a,b) for(ll i=(ll)a;i<(ll)b;i++)
#define rf(i,a,b) for(ll i=(ll)a;i>=(ll)b;i--)
#define fa(x,v) for(auto x:v)
#define INF (ll)(9e18)
#define Sort(v) sort(v.begin(),v.end())
#define rsort(v) sort(v.rbegin(),v.rend())
#define test ll T;cin>>T;while(T--)
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define db1(x) cout<<#x<<"="<<x<<'\n'
#define db2(x,y) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<'\n'
#define db3(x,y,z) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<","<<#z<<"="<<z<<'\n'
#define db4(x,y,z,w) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<","<<#z<<"="<<z<<","<<#w<<"="<<w<<'\n'
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define max4(a,b,c,d) max(a,max3(b,c,d))
#define min4(a,b,c,d) min(a,min3(b,c,d))
#define maxi(a) *max_element(a,a+n)
#define mini(a) *min_element(a,a+n)
#define no cout << "NO" << endl
#define yes cout << "YES" << endl
#define no2 cout << "No" << endl
#define yes2 cout << "Yes" << endl
#define mxheap    priority_queue<int>
#define mnheap    priority_queue<int,vector<int>,greater<int>>
#define lb(v,val)  (lower_bound(v.begin(),v.end(),val)-v.begin())
#define ub(v,val)  (upper_bound(v.begin(),v.end(),val)-v.begin())
 const ll MOD=1000000000+7;
const ll MOD1 = 998244353;

string itos(ll s)
{
string str=to_string(s);
return str;
}
ll stoi2(string s)
{
    ll a= atoi(s.c_str());
    return a;
}
template <typename T>
void read(T &p)
{
    cin >> p;
}
 
template <typename T, typename T1>
void read(pair<T, T1> &p)
{
    read(p.ff);
    read(p.ss);
}
 
template <typename T>
void read(T arr[], ll n)
{
    for (ll i = 0; i < n; i++)
    {
        read(arr[i]);
    }
}
 
template <typename T>
void read(vector<T> &arr)
{
    for (ll i = 0; i < arr.size(); i++)
    {
        read(arr[i]);
    }
}
//////////////////////////////////////
 
template <typename T>
void out(T& n)
{
    cout << n;
}
 
template <typename T, typename T1>
void out(pair<T, T1> &p)
{
    cout << "(";
    out(p.ff);
    cout << ",";
    out(p.ss);
    cout << ")";
    cout<<endl;
}
 
template <typename T>
void out(T arr[], ll n)
{
    for (ll i = 0; i < n; i++)
    {
        out(arr[i]);
        cout << " ";
    }
    cout<<endl;
}
 
template <typename T>
void out(vector<T> &arr)
{
 
    for (ll i = 0; i < arr.size(); i++)
    {
        out(arr[i]);
        if (i!=arr.size()-1)
            cout << " ";
    }
    cout<<endl;
 
}
 
 
 
template <typename T>
void out(set<T> &arr)
{
    for (auto i:arr)
    {
        out(i);
        cout << " ";
    }
    cout<<endl;
}
 
template <typename T>
void out(multiset<T> &arr)
{
    for (auto i:arr)
    {
        out(i);
        cout << " ";
    }
    cout<<endl;
}
 
template <typename T, typename T1>
void out(map<T,T1> &m)
{
    for (auto i:m)
    {
        out(i.first);
        cout<<" -> ";
        out(i.second);
        cout<<", ";
    }
    cout<<endl;
}
ll powerm(ll a, ll b, ll MOD) {
    a %= MOD;
    ll res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}

ll power(ll a, ll b) {
   
  ll res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a ;
        a = a * a ;
        b >>= 1;
    }
    return res;
}

bool isSubSequence(string str1, string str2, int m, int n)
{

    if (m == 0) return true;
    if (n == 0) return false;

    if (str1[m-1] == str2[n-1])
        return isSubSequence(str1, str2, m-1, n-1);

    return isSubSequence(str1, str2, m, n-1);
}


bool ispalindrome(ll len,string str)
{
 
    for(int i = 0; i < len/2; i++){
        if(str[i] != str[len-1-i]){
            return false;
        }
    }
    return true;
}
inline bool isPowerOfTwo(ll x)
{
    return ((1LL << (ll)log2(x)) == x);
}
ll isprime(ll N){
    if(N<2 || (!(N&1) && N!=2))
        return 0;
    for(ll i=3; i*i<=N; i+=2){
        if(!(N%i))
            return 0;
    }
    return 1;
}
vec factor;
void factors(ll n)
{
    
for(ll i=1;i<=sqrt(n);i++)
{
    if(n%i==0)
    {
        if(i==n/i)
        factor.pb(i);
        else
        {
            factor.pb(i);
            factor.pb(n/i);
        }
        
    }
}
 
sort(all(factor));
}
ll gcd(ll a, ll b) { 
   if (b == 0)  
      return a; 
   return gcd(b, a % b);  
}
ll lcm(ll a,ll b)
{
    return (a/gcd(a,b))*b;
}
bool isvalid(ll i,ll j,ll n)
{
    if(i>=0&&i<n&&j>=0&&j<n)return true;
    return false;
}
ll dx[8]={0,1,1,1,0,-1,-1,-1};
ll dy[8]={-1,-1,0,1,1,1,0,-1};


ll binarytodecimal(string n)
{
    string num = n;
    ll dec_value = 0;
 
   ll base = 1;
 
   ll len = num.length();
    for (int i = len - 1; i >= 0; i--) {
        if (num[i] == '1')
            dec_value += base;
        base = base * 2;
    }
 
    return dec_value;
}
ll extended_GCD(ll a , ll b , ll &x , ll &y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    ll x1 , y1;
    ll gcd = extended_GCD(b % a , a , x1 , y1);
    x = y1 - (b / a) * x1;
    y = x1;
    return gcd;
}
ll modinv(ll a , ll mod = MOD) {
    ll x , y;
    extended_GCD(a , mod , x , y);
    if (x < 0) x += mod;
    return x;
}
string dtb(ll  n )
{

    string s="";

    while(n>0){

    if(n%2==0)s.pb('0');
    else s.pb('1');
    n/=2;

    }

    reverse(all(s));
//       while(s.size()<siz)
//    {
//
//        s='0'+s;
//
//    }
    return s;
}
ll getfactorisation(ll n)
{
ll N=5e6+5;
  vector<ll>fact(N);
  for(int i=0;i<N;i++)fact[i]=i;
  for(int i=2;i<N;i+=2)fact[i]=2;
      for (ll i=3;i<= N ;i+= 2)
       if (i==fact[i])
        for (ll j=i*i ; j<N;j+= i)
         if (fact[j]== j)fact[j] = i;

vec res;
  while(n>1)
  {
     res.pb(fact[n]);
      n/=fact[n];


  }
  return res.size();
}

long long maxPrimeFactor(long long n) 
{ 
    long long maxPrime = -1; 
  
    while (n % 2 == 0) { 
        maxPrime = 2; 
        n >>= 1; // equivalent to n /= 2 
    } 
  
    for (int i = 3; i <= sqrt(n); i += 2) { 
        while (n % i == 0) { 
            maxPrime = i; 
            n = n / i; 
        } 
    } 
  
    if (n > 2) 
        maxPrime = n; 
  
    return maxPrime; 
} 

vec seive;
void Seive() {
    const ll maxn = 1e6 + 5;
    seive.resize(maxn);
    f(i,0, maxn) seive[i] = i;
    for(ll i=2;i<=maxn;i+=2)
    seive[i] = 2;
    seive[1] = -1;
    seive[0] = -1;
    for (ll i = 3; i <= maxn; i += 2)
        if (i == seive[i])
        for (ll j = i * i ; j < maxn ; j += i)
        if (seive[j] == j)
        seive[j] = i;
}
//cout<<"Case #"<<t<<": ";
// check integer overflow(s->x+y--s<x)
void factorisation(ll n)
{
vec res;
     for(ll i=2;i*i<=n;i++) {
            if (n%i==0) {
                while (n%i==0) {
                    n/=i;
                   res.pb(i);
                }
            }
        }
        if (n>1)
            res.pb(n);

}
 int numOfDivisors[100005]={0};
   void noOfDivisor(){
    for(int i=1;i<=100005;i++)
        for(int j=i;j<=100005;j+=i){
            numOfDivisors[j]++;
        }
}

ll fac[200005];
unsigned long long modInverse(unsigned long long n,  
                                            int p)
{
    return powerm(n, p - 2, p);
}
  long long nCrModPFermat(unsigned long long n,
                                 int r, int p)
{
    if (n < r)
        return 0;
    if (r == 0)
        return 1;
 unsigned long long fac[n + 1];
    fac[0] = 1;
    for (int i = 1; i <= n; i++)
        fac[i] = (fac[i - 1] * i) % p;
 
    return (fac[n] * modInverse(fac[r], p) % p
            * modInverse(fac[n - r], p) % p)
           % p;
}

int main()
{
fast;

 
 ll T=1;
  cin>>T;
while(T--)
{
  ll n,m,x;
  cin>>n>>m>>x;
  vec v(n,0);
  ll sum=0;
  f(i,0,n)cin>>v[i],sum+=v[i];

  VP p;
  f(i,0,n)
  {
    p.pb({v[i],i});
  }
  Sort(p);
  reverse(all(p));
  mll mp;
   ll cur=1;
   for(int i=0;i<n;i++)
   {
        mp[p[i].ss]=cur;
        cur++;
        if(cur>m)cur=1;
   }
   yes;
   f(i,0,n)
    cout<<mp[i]<<MM;
en;


}















    
}