Polycarp took $n$ videos, the duration of the $i$-th video is $a_i$ seconds. The videos are listed in the chronological order, i.e. the $1$-st video is the earliest, the $2$-nd video is the next, ..., the $n$-th video is the last.

Now Polycarp wants to publish exactly $k$ ($1 \le k \le n$) posts in Instabram. Each video should be a part of a single post. The posts should preserve the chronological order, it means that the first post should contain one or more of the earliest videos, the second post should contain a block (one or more videos) going next and so on. In other words, if the number of videos in the $j$-th post is $s_j$ then:

  $s_1+s_2+\dots+s_k=n$ ($s_i>0$),  the first post contains the videos: $1, 2, \dots, s_1$;  the second post contains the videos: $s_1+1, s_1+2, \dots, s_1+s_2$;  the third post contains the videos: $s_1+s_2+1, s_1+s_2+2, \dots, s_1+s_2+s_3$;  ...  the $k$-th post contains videos: $n-s_k+1,n-s_k+2,\dots,n$. 

Polycarp is a perfectionist, he wants the total duration of videos in each post to be the same.

Help Polycarp to find such positive integer values $s_1, s_2, \dots, s_k$ that satisfy all the conditions above.


-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 10^5$). The next line contains $n$ positive integer numbers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^4$), where $a_i$ is the duration of the $i$-th video.


-----Output-----

If solution exists, print "Yes" in the first line. Print $k$ positive integers $s_1, s_2, \dots, s_k$ ($s_1+s_2+\dots+s_k=n$) in the second line. The total duration of videos in each post should be the same. It can be easily proven that the answer is unique (if it exists).

If there is no solution, print a single line "No".


-----Examples-----
Input
6 3
3 3 1 4 1 6

Output
Yes
2 3 1 
Input
3 3
1 1 1

Output
Yes
1 1 1 
Input
3 3
1 1 2

Output
No
Input
3 1
1 10 100

Output
Yes
3

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'n, k = [int(x) for x in input().split()]\na = [int(x) for x in input().split()]\ns = sum(a)\nif s % k != 0:\n    print("No")\n    return\nrvl = s // k\nvip =[]\ntvip = 0\ntvipl = 0\nfor cv in range(n):\n    tvip += 1\n    tvipl += a[cv]\n    if tvipl > rvl:\n        print("No")\n        return\n    elif tvipl == rvl:\n        vip.append(tvip)\n        tvip = 0\n        tvipl = 0\nprint("Yes")\nprint(*vip, sep=\' \')\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: