1521_A. Nastia and Nearly Good Numbers_28911
Nastia has 2 positive integers A and B. She defines that:

  * The integer is good if it is divisible by A ⋅ B; 
  * Otherwise, the integer is nearly good, if it is divisible by A. 



For example, if A = 6 and B = 4, the integers 24 and 72 are good, the integers 6, 660 and 12 are nearly good, the integers 16, 7 are neither good nor nearly good.

Find 3 different positive integers x, y, and z such that exactly one of them is good and the other 2 are nearly good, and x + y = z.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains two integers A and B (1 ≤ A ≤ 10^6, 1 ≤ B ≤ 10^6) — numbers that Nastia has.

Output

For each test case print: 

  * "YES" and 3 different positive integers x, y, and z (1 ≤ x, y, z ≤ 10^{18}) such that exactly one of them is good and the other 2 are nearly good, and x + y = z. 
  * "NO" if no answer exists. 

You can print each character of "YES" or "NO" in any case.

If there are multiple answers, print any.

Example

Input


3
5 3
13 2
7 11


Output


YES
10 50 60
YES
169 39 208
YES
28 154 182

Note

In the first test case: 60 — good number; 10 and 50 — nearly good numbers.

In the second test case: 208 — good number; 169 and 39 — nearly good numbers.

In the third test case: 154 — good number; 28 and 182 — nearly good numbers.
#include<bits/stdc++.h>
using namespace std;
#define dd double
#define ll long long int
#define pb push_back
#define mp make_pair
#define fi first
#define sc second
#define pr pair<ll,ll>
#define pri pair<pr,ll>
#define pir pair<ll,pr>
#define ppr pair<pr,pr>
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
ll mod=1e9+7;
ll INF=9e18;
ll gcde(ll a, ll b) {
    return b ? gcde (b, a % b) : a;
}
int main()
{
   #ifndef ONLINE_JUDGE
   freopen("inp.txt","r",stdin);
   freopen("otpt.txt","w",stdout);
   #endif
   fastio;
   ll te=1;
   cin>>te;
   while(te--)
   {
       ll a,b,i,j,t;
       cin>>a>>b;
       ll x=a;
       if(b==1)
       {
        cout<<"NO"<<endl;
        continue;
       }
       ll y=a*b;
       ll z=x+y;
       cout<<"YES"<<endl;
       cout<<x<<" "<<y<<" "<<z<<endl;
   } 
}

//CHECKED FOR OVERFLOWS??
//CHECKED FOR EDGE CONDITION??
3
5 3
13 2
7 11
 3
5 3
13 2
7 11
 3
5 3
13 2
14 11
 3
5 3
4 2
7 11
 3
7 3
13 2
14 11
 3
5 3
6 2
7 11
 3
5 4
6 2
7 11
 3
5 4
3 2
7 11
 3
5 6
13 2
7 11
 3
5 3
13 2
7 19
 3
5 3
21 2
14 11
 3
5 3
4 2
7 3
 3
7 3
13 2
16 11
 3
5 3
6 2
7 3
 3
5 4
3 2
7 19
 3
5 6
9 2
7 11
 3
5 3
13 2
7 35
 3
5 3
21 2
14 22
 3
10 3
4 2
7 3
 3
7 3
13 2
17 11
 3
7 3
6 2
7 3
 3
5 4
3 2
7 31
 3
5 10
9 2
7 11
 3
5 3
13 4
7 35
 3
5 3
21 3
14 22
 3
10 3
4 2
8 3
 3
2 3
6 2
7 3
 3
5 4
6 2
7 31
 3
5 10
1 2
7 11
 3
5 3
13 4
7 22
 3
2 3
21 3
14 22
 3
2 3
7 2
7 3
 3
5 4
6 2
7 43
 3
5 3
13 4
7 16
 3
2 3
21 3
14 20
 3
2 3
7 4
7 3
 3
5 3
6 2
7 43
 3
5 3
13 4
14 16
 3
2 3
21 2
14 20
 3
2 3
7 4
10 3
 3
5 3
6 2
7 74
 3
5 3
13 6
14 16
 3
2 3
21 2
14 6
 3
2 3
7 4
10 6
 3
5 3
13 6
26 16
 3
2 3
21 2
19 6
 3
2 3
7 4
10 7
 3
5 3
13 6
24 16
 3
4 3
21 2
19 6
 3
4 3
7 4
10 7
 3
5 3
13 6
15 16
 3
2 3
3 2
19 6
 3
4 3
7 4
17 7
 3
1 3
13 6
15 16
 3
1 3
3 2
19 6
 3
4 3
7 6
17 7
 3
1 3
13 6
15 7
 3
1 3
3 2
26 6
 3
5 3
7 6
17 7
 3
1 3
13 6
15 14
 3
5 3
10 6
17 7
 3
1 3
13 6
15 23
 3
6 3
10 6
17 7
 3
1 3
13 6
20 23
 3
6 3
10 11
17 7
 3
1 3
13 6
3 23
 3
8 3
10 11
17 7
 3
1 3
13 6
6 23
 3
8 3
10 11
14 7
 3
2 3
13 6
6 23
 3
8 3
4 11
14 7
 3
3 3
13 6
6 23
 3
6 3
13 6
6 23
 3
6 3
13 6
1 23
 3
6 3
13 6
1 6
 3
6 3
13 12
1 6
 3
6 3
19 12
1 6
 3
6 1
19 12
1 6
 3
6 1
19 14
1 6
 3
5 3
13 2
9 11
 3
5 3
16 2
7 11
 3
5 3
24 2
14 11
 3
5 4
6 2
14 11
 3
8 6
13 2
7 11
 3
5 3
13 2
7 7
 3
4 3
21 2
14 11
 3
7 3
13 3
16 11
 3
5 3
6 2
7 2
 3
5 4
3 3
7 19
 3
5 6
4 2
7 11
 3
5 4
13 2
7 35
 3
10 3
21 2
14 22
 3
10 3
3 2
7 3
 3
7 3
13 2
17 9
 3
5 4
3 2
8 31
 3
5 10
9 2
6 11
 3
5 3
11 4
7 35
 3
5 3
34 3
14 22
 3
10 2
4 2
8 3
 3
5 8
6 2
7 31
 3
2 10
1 2
7 11
 3
2 3
6 3
14 22
 3
2 2
7 2
7 3
 3
5 6
6 2
7 43
 3
6 3
13 4
7 16
 3
2 3
21 3
14 2
 3
3 3
7 4
7 3
 3
2 3
21 2
14 7
 3
3 3
7 4
10 3
 3
5 3
6 2
7 58
 3
5 3
26 6
14 16
 3
2 3
7 4
10 5
 3
5 3
13 6
26 20
 3
2 3
41 2
19 6
 3
2 2
7 4
10 7
 3
5 3
13 6
7 16
 3
4 3
21 4
19 6
 3
4 3
7 4
19 7
 3
5 3
13 6
15 7
 3
4 3
6 4
17 7
 3
1 3
5 2
19 6
 3
1 3
16 6
15 14
 3
1 3
3 2
25 6
 3
5 3
12 6
17 7
 3
1 3
13 6
15 3
 3
5 3
10 6
20 7
 3
1 3
13 6
21 23
 3
6 3
10 6
17 10
 3
1 3
13 8
20 23
 3
6 3
3 11
17 7
 3
1 3
13 11
3 23
 3
8 3
10 21
17 7
 3
2 4
13 6
6 23
 3
8 3
10 11
14 3
 3
2 3
13 1
6 23
 3
8 3
4 13
14 7
 3
3 6
13 6
6 23
 3
6 3
16 6
1 23
 3
6 3
13 6
1 4
 3
6 3
8 12
1 6
 3
6 3
19 16
1 6
 3
5 3
13 2
9 5
 3
5 3
16 2
7 8
 3
5 3
24 2
14 21
 3
5 4
6 4
14 11
 3
5 6
13 2
13 11
 3
2 3
13 2
7 7
 3
4 3
21 2
5 11
 3
7 3
13 3
16 12
 3
5 3
6 2
7 4
 3
5 4
1 3
7 19
 3
5 4
13 2
7 42
 3
10 3
34 2
14 22
 3
10 5
4 2
7 3
 3
13 3
13 2
17 9
 3
7 4
3 2
8 31
 3
5 10
13 2
6 11
 3
5 3
5 4
7 35
 3
5 3
34 3
10 22
 3
10 2
8 2
8 3
 3
5 8
6 2
3 31
 3
2 10
1 3
7 11
 3
2 3
6 3
14 32
 3
2 2
7 2
10 3
 3
3 6
6 2
7 43
 3
6 3
13 8
7 16
 3
2 3
21 3
3 2
 3
3 3
13 4
7 3
 3
2 3
21 2
17 7
 3
3 6
7 4
10 3
 3
5 3
3 2
7 58
 3
5 3
26 6
16 16
 3
2 3
3 4
10 7
 3
5 3
13 6
38 20
 3
5 3
13 6
12 16
 3
3 3
21 4
19 6
 3
4 3
7 4
19 1
 3
5 3
7 6
15 7
 3
4 4
6 4
17 7
 3
1 3
5 2
31 6
 3
1 3
16 6
15 28
 3
1 1
3 2
25 6
 3
5 3
12 6
17 8
 3
1 6
13 6
15 3
 3
6 3
10 6
20 7
 3
1 3
13 8
21 23
 3
6 5
10 6
17 10
 3
1 3
13 10
20 23
 3
6 3
3 2
17 7
 3
1 3
15 11
3 23
 3
8 3
1 21
17 7
 3
2 4
21 6
6 23
 3
8 3
10 21
14 3
 3
2 1
13 1
6 23
 3
8 3
4 13
11 7
 3
6 6
13 6
6 23
 3
4 3
16 6
1 23
 3
5 3
13 6
1 4
 3
9 3
8 12
1 6
 3
12 3
19 16
1 6
 3
5 3
7 2
9 5
 3
5 3
16 2
7 15


YES
10 50 60
YES
169 39 208
YES
28 154 182 YES
5 15 20
YES
13 26 39
YES
7 77 84
 YES
5 15 20
YES
13 26 39
YES
14 154 168
 YES
5 15 20
YES
4 8 12
YES
7 77 84
 YES
7 21 28
YES
13 26 39
YES
14 154 168
 YES
5 15 20
YES
6 12 18
YES
7 77 84
 YES
5 20 25
YES
6 12 18
YES
7 77 84
 YES
5 20 25
YES
3 6 9
YES
7 77 84
 YES
5 30 35
YES
13 26 39
YES
7 77 84
 YES
5 15 20
YES
13 26 39
YES
7 133 140
 YES
5 15 20
YES
21 42 63
YES
14 154 168
 YES
5 15 20
YES
4 8 12
YES
7 21 28
 YES
7 21 28
YES
13 26 39
YES
16 176 192
 YES
5 15 20
YES
6 12 18
YES
7 21 28
 YES
5 20 25
YES
3 6 9
YES
7 133 140
 YES
5 30 35
YES
9 18 27
YES
7 77 84
 YES
5 15 20
YES
13 26 39
YES
7 245 252
 YES
5 15 20
YES
21 42 63
YES
14 308 322
 YES
10 30 40
YES
4 8 12
YES
7 21 28
 YES
7 21 28
YES
13 26 39
YES
17 187 204
 YES
7 21 28
YES
6 12 18
YES
7 21 28
 YES
5 20 25
YES
3 6 9
YES
7 217 224
 YES
5 50 55
YES
9 18 27
YES
7 77 84
 YES
5 15 20
YES
13 52 65
YES
7 245 252
 YES
5 15 20
YES
21 63 84
YES
14 308 322
 YES
10 30 40
YES
4 8 12
YES
8 24 32
 YES
2 6 8
YES
6 12 18
YES
7 21 28
 YES
5 20 25
YES
6 12 18
YES
7 217 224
 YES
5 50 55
YES
1 2 3
YES
7 77 84
 YES
5 15 20
YES
13 52 65
YES
7 154 161
 YES
2 6 8
YES
21 63 84
YES
14 308 322
 YES
2 6 8
YES
7 14 21
YES
7 21 28
 YES
5 20 25
YES
6 12 18
YES
7 301 308
 YES
5 15 20
YES
13 52 65
YES
7 112 119
 YES
2 6 8
YES
21 63 84
YES
14 280 294
 YES
2 6 8
YES
7 28 35
YES
7 21 28
 YES
5 15 20
YES
6 12 18
YES
7 301 308
 YES
5 15 20
YES
13 52 65
YES
14 224 238
 YES
2 6 8
YES
21 42 63
YES
14 280 294
 YES
2 6 8
YES
7 28 35
YES
10 30 40
 YES
5 15 20
YES
6 12 18
YES
7 518 525
 YES
5 15 20
YES
13 78 91
YES
14 224 238
 YES
2 6 8
YES
21 42 63
YES
14 84 98
 YES
2 6 8
YES
7 28 35
YES
10 60 70
 YES
5 15 20
YES
13 78 91
YES
26 416 442
 YES
2 6 8
YES
21 42 63
YES
19 114 133
 YES
2 6 8
YES
7 28 35
YES
10 70 80
 YES
5 15 20
YES
13 78 91
YES
24 384 408
 YES
4 12 16
YES
21 42 63
YES
19 114 133
 YES
4 12 16
YES
7 28 35
YES
10 70 80
 YES
5 15 20
YES
13 78 91
YES
15 240 255
 YES
2 6 8
YES
3 6 9
YES
19 114 133
 YES
4 12 16
YES
7 28 35
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
15 240 255
 YES
1 3 4
YES
3 6 9
YES
19 114 133
 YES
4 12 16
YES
7 42 49
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
15 105 120
 YES
1 3 4
YES
3 6 9
YES
26 156 182
 YES
5 15 20
YES
7 42 49
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
15 210 225
 YES
5 15 20
YES
10 60 70
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
15 345 360
 YES
6 18 24
YES
10 60 70
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
20 460 480
 YES
6 18 24
YES
10 110 120
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
3 69 72
 YES
8 24 32
YES
10 110 120
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
6 138 144
 YES
8 24 32
YES
10 110 120
YES
14 98 112
 YES
2 6 8
YES
13 78 91
YES
6 138 144
 YES
8 24 32
YES
4 44 48
YES
14 98 112
 YES
3 9 12
YES
13 78 91
YES
6 138 144
 YES
6 18 24
YES
13 78 91
YES
6 138 144
 YES
6 18 24
YES
13 78 91
YES
1 23 24
 YES
6 18 24
YES
13 78 91
YES
1 6 7
 YES
6 18 24
YES
13 156 169
YES
1 6 7
 YES
6 18 24
YES
19 228 247
YES
1 6 7
 NO
YES
19 228 247
YES
1 6 7
 NO
YES
19 266 285
YES
1 6 7
 YES
5 15 20
YES
13 26 39
YES
9 99 108
 YES
5 15 20
YES
16 32 48
YES
7 77 84
 YES
5 15 20
YES
24 48 72
YES
14 154 168
 YES
5 20 25
YES
6 12 18
YES
14 154 168
 YES
8 48 56
YES
13 26 39
YES
7 77 84
 YES
5 15 20
YES
13 26 39
YES
7 49 56
 YES
4 12 16
YES
21 42 63
YES
14 154 168
 YES
7 21 28
YES
13 39 52
YES
16 176 192
 YES
5 15 20
YES
6 12 18
YES
7 14 21
 YES
5 20 25
YES
3 9 12
YES
7 133 140
 YES
5 30 35
YES
4 8 12
YES
7 77 84
 YES
5 20 25
YES
13 26 39
YES
7 245 252
 YES
10 30 40
YES
21 42 63
YES
14 308 322
 YES
10 30 40
YES
3 6 9
YES
7 21 28
 YES
7 21 28
YES
13 26 39
YES
17 153 170
 YES
5 20 25
YES
3 6 9
YES
8 248 256
 YES
5 50 55
YES
9 18 27
YES
6 66 72
 YES
5 15 20
YES
11 44 55
YES
7 245 252
 YES
5 15 20
YES
34 102 136
YES
14 308 322
 YES
10 20 30
YES
4 8 12
YES
8 24 32
 YES
5 40 45
YES
6 12 18
YES
7 217 224
 YES
2 20 22
YES
1 2 3
YES
7 77 84
 YES
2 6 8
YES
6 18 24
YES
14 308 322
 YES
2 4 6
YES
7 14 21
YES
7 21 28
 YES
5 30 35
YES
6 12 18
YES
7 301 308
 YES
6 18 24
YES
13 52 65
YES
7 112 119
 YES
2 6 8
YES
21 63 84
YES
14 28 42
 YES
3 9 12
YES
7 28 35
YES
7 21 28
 YES
2 6 8
YES
21 42 63
YES
14 98 112
 YES
3 9 12
YES
7 28 35
YES
10 30 40
 YES
5 15 20
YES
6 12 18
YES
7 406 413
 YES
5 15 20
YES
26 156 182
YES
14 224 238
 YES
2 6 8
YES
7 28 35
YES
10 50 60
 YES
5 15 20
YES
13 78 91
YES
26 520 546
 YES
2 6 8
YES
41 82 123
YES
19 114 133
 YES
2 4 6
YES
7 28 35
YES
10 70 80
 YES
5 15 20
YES
13 78 91
YES
7 112 119
 YES
4 12 16
YES
21 84 105
YES
19 114 133
 YES
4 12 16
YES
7 28 35
YES
19 133 152
 YES
5 15 20
YES
13 78 91
YES
15 105 120
 YES
4 12 16
YES
6 24 30
YES
17 119 136
 YES
1 3 4
YES
5 10 15
YES
19 114 133
 YES
1 3 4
YES
16 96 112
YES
15 210 225
 YES
1 3 4
YES
3 6 9
YES
25 150 175
 YES
5 15 20
YES
12 72 84
YES
17 119 136
 YES
1 3 4
YES
13 78 91
YES
15 45 60
 YES
5 15 20
YES
10 60 70
YES
20 140 160
 YES
1 3 4
YES
13 78 91
YES
21 483 504
 YES
6 18 24
YES
10 60 70
YES
17 170 187
 YES
1 3 4
YES
13 104 117
YES
20 460 480
 YES
6 18 24
YES
3 33 36
YES
17 119 136
 YES
1 3 4
YES
13 143 156
YES
3 69 72
 YES
8 24 32
YES
10 210 220
YES
17 119 136
 YES
2 8 10
YES
13 78 91
YES
6 138 144
 YES
8 24 32
YES
10 110 120
YES
14 42 56
 YES
2 6 8
NO
YES
6 138 144
 YES
8 24 32
YES
4 52 56
YES
14 98 112
 YES
3 18 21
YES
13 78 91
YES
6 138 144
 YES
6 18 24
YES
16 96 112
YES
1 23 24
 YES
6 18 24
YES
13 78 91
YES
1 4 5
 YES
6 18 24
YES
8 96 104
YES
1 6 7
 YES
6 18 24
YES
19 304 323
YES
1 6 7
 YES
5 15 20
YES
13 26 39
YES
9 45 54
 YES
5 15 20
YES
16 32 48
YES
7 56 63
 YES
5 15 20
YES
24 48 72
YES
14 294 308
 YES
5 20 25
YES
6 24 30
YES
14 154 168
 YES
5 30 35
YES
13 26 39
YES
13 143 156
 YES
2 6 8
YES
13 26 39
YES
7 49 56
 YES
4 12 16
YES
21 42 63
YES
5 55 60
 YES
7 21 28
YES
13 39 52
YES
16 192 208
 YES
5 15 20
YES
6 12 18
YES
7 28 35
 YES
5 20 25
YES
1 3 4
YES
7 133 140
 YES
5 20 25
YES
13 26 39
YES
7 294 301
 YES
10 30 40
YES
34 68 102
YES
14 308 322
 YES
10 50 60
YES
4 8 12
YES
7 21 28
 YES
13 39 52
YES
13 26 39
YES
17 153 170
 YES
7 28 35
YES
3 6 9
YES
8 248 256
 YES
5 50 55
YES
13 26 39
YES
6 66 72
 YES
5 15 20
YES
5 20 25
YES
7 245 252
 YES
5 15 20
YES
34 102 136
YES
10 220 230
 YES
10 20 30
YES
8 16 24
YES
8 24 32
 YES
5 40 45
YES
6 12 18
YES
3 93 96
 YES
2 20 22
YES
1 3 4
YES
7 77 84
 YES
2 6 8
YES
6 18 24
YES
14 448 462
 YES
2 4 6
YES
7 14 21
YES
10 30 40
 YES
3 18 21
YES
6 12 18
YES
7 301 308
 YES
6 18 24
YES
13 104 117
YES
7 112 119
 YES
2 6 8
YES
21 63 84
YES
3 6 9
 YES
3 9 12
YES
13 52 65
YES
7 21 28
 YES
2 6 8
YES
21 42 63
YES
17 119 136
 YES
3 18 21
YES
7 28 35
YES
10 30 40
 YES
5 15 20
YES
3 6 9
YES
7 406 413
 YES
5 15 20
YES
26 156 182
YES
16 256 272
 YES
2 6 8
YES
3 12 15
YES
10 70 80
 YES
5 15 20
YES
13 78 91
YES
38 760 798
 YES
5 15 20
YES
13 78 91
YES
12 192 204
 YES
3 9 12
YES
21 84 105
YES
19 114 133
 YES
4 12 16
YES
7 28 35
NO
 YES
5 15 20
YES
7 42 49
YES
15 105 120
 YES
4 16 20
YES
6 24 30
YES
17 119 136
 YES
1 3 4
YES
5 10 15
YES
31 186 217
 YES
1 3 4
YES
16 96 112
YES
15 420 435
 NO
YES
3 6 9
YES
25 150 175
 YES
5 15 20
YES
12 72 84
YES
17 136 153
 YES
1 6 7
YES
13 78 91
YES
15 45 60
 YES
6 18 24
YES
10 60 70
YES
20 140 160
 YES
1 3 4
YES
13 104 117
YES
21 483 504
 YES
6 30 36
YES
10 60 70
YES
17 170 187
 YES
1 3 4
YES
13 130 143
YES
20 460 480
 YES
6 18 24
YES
3 6 9
YES
17 119 136
 YES
1 3 4
YES
15 165 180
YES
3 69 72
 YES
8 24 32
YES
1 21 22
YES
17 119 136
 YES
2 8 10
YES
21 126 147
YES
6 138 144
 YES
8 24 32
YES
10 210 220
YES
14 42 56
 NO
NO
YES
6 138 144
 YES
8 24 32
YES
4 52 56
YES
11 77 88
 YES
6 36 42
YES
13 78 91
YES
6 138 144
 YES
4 12 16
YES
16 96 112
YES
1 23 24
 YES
5 15 20
YES
13 78 91
YES
1 4 5
 YES
9 27 36
YES
8 96 104
YES
1 6 7
 YES
12 36 48
YES
19 304 323
YES
1 6 7
 YES
5 15 20
YES
7 14 21
YES
9 45 54
 YES
5 15 20
YES
16 32 48
YES
7 105 112
