Levko loves array a_1, a_2, ... , a_{n}, consisting of integers, very much. That is why Levko is playing with array a, performing all sorts of operations with it. Each operation Levko performs is of one of two types:

  Increase all elements from l_{i} to r_{i} by d_{i}. In other words, perform assignments a_{j} = a_{j} + d_{i} for all j that meet the inequation l_{i} ≤ j ≤ r_{i}.  Find the maximum of elements from l_{i} to r_{i}. That is, calculate the value $m_{i} = \operatorname{max}_{j = l_{i}}^{r_{i}} a_{j}$. 

Sadly, Levko has recently lost his array. Fortunately, Levko has records of all operations he has performed on array a. Help Levko, given the operation records, find at least one suitable array. The results of all operations for the given array must coincide with the record results. Levko clearly remembers that all numbers in his array didn't exceed 10^9 in their absolute value, so he asks you to find such an array.


-----Input-----

The first line contains two integers n and m (1 ≤ n, m ≤ 5000) — the size of the array and the number of operations in Levko's records, correspondingly.

Next m lines describe the operations, the i-th line describes the i-th operation. The first integer in the i-th line is integer t_{i} (1 ≤ t_{i} ≤ 2) that describes the operation type. If t_{i} = 1, then it is followed by three integers l_{i}, r_{i} and d_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n,  - 10^4 ≤ d_{i} ≤ 10^4) — the description of the operation of the first type. If t_{i} = 2, then it is followed by three integers l_{i}, r_{i} and m_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n,  - 5·10^7 ≤ m_{i} ≤ 5·10^7) — the description of the operation of the second type.

The operations are given in the order Levko performed them on his array.


-----Output-----

In the first line print "YES" (without the quotes), if the solution exists and "NO" (without the quotes) otherwise.

If the solution exists, then on the second line print n integers a_1, a_2, ... , a_{n} (|a_{i}| ≤ 10^9) — the recovered array.


-----Examples-----
Input
4 5
1 2 3 1
2 1 2 8
2 3 4 7
1 1 3 3
2 3 4 8

Output
YES
4 7 4 7
Input
4 5
1 2 3 1
2 1 2 8
2 3 4 7
1 1 3 3
2 3 4 13

Output
NO

```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, m = map(int, input().split())\na = [10**9 for _ in range(n)]\nextra = [0 for _ in range(n)]\nquery = list()\nfor _ in range(m):\n     t, l, r, x = map(int, input().split())\n     l -= 1\n     r -= 1\n     query.append((t, l, r, x))\n     if t == 1:\n          for j in range(l, r + 1):\n               extra[j] += x\n     else:\n          for j in range(l, r + 1):\n               a[j] = min(a[j], x - extra[j])\nextra = a.copy()\nfor t, l, r, x in query:\n     if t == 1:\n          for j in range(l, r + 1):\n               a[j] += x\n     else:\n          val = -10**9\n          for j in range(l, r + 1):\n               val = max(val, a[j])\n          if not val == x:\n               print('NO')\n               return\n\nprint('YES')\nfor x in extra:\n     print(x, end=' ')\n          "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: