361_C. Levko and Array Recovery
Levko loves array a1, a2, ... , an, 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:

  1. Increase all elements from li to ri by di. In other words, perform assignments aj = aj + di for all j that meet the inequation li ≤ j ≤ ri. 
  2. Find the maximum of elements from li to ri. That is, calculate the value <image>. 



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 109 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 ti (1 ≤ ti ≤ 2) that describes the operation type. If ti = 1, then it is followed by three integers li, ri and di (1 ≤ li ≤ ri ≤ n,  - 104 ≤ di ≤ 104) — the description of the operation of the first type. If ti = 2, then it is followed by three integers li, ri and mi (1 ≤ li ≤ ri ≤ n,  - 5·107 ≤ mi ≤ 5·107) — 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 a1, a2, ... , an (|ai| ≤ 109) — 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
import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**9+7

Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()

n,m = Ri()
lis = []
for i in range(m):
    lis.append(Ri())
ans = [10**9]*n
for i in range(m-1,-1,-1):
    if lis[i][0] == 2:
        for j in range(lis[i][1]-1,lis[i][2]):
            ans[j] = min(ans[j], lis[i][3])
    else:
        for j in range(lis[i][1]-1,lis[i][2]):
            if ans[j] != 10**9:
                ans[j]-=lis[i][3]

for i in range(n):
    if ans[i] == 10**9:
        ans[i] = -10**9
temp = ans[:]
# print(temp)
flag = True
for i in range(m):
    if lis[i][0] == 2:
        t= -10**9
        for j in range(lis[i][1]-1,lis[i][2]):
            t = max(t, temp[j])
        if t != lis[i][3]:
            flag = False
            break
    else:
        for j in range(lis[i][1]-1,lis[i][2]):
            temp[j]+=lis[i][3]
# print(temp, ans)
if flag :
    YES()
    print(*ans)
else:
    NO()
    # print(-1)
```