Problem: You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

* `0 l r b c`: For each i = l, l+1, \dots, {r - 1}, set a_i \gets b \times a_i + c.
* `1 l r`: Print \sum_{i = l}^{r - 1} a_i \bmod 998244353.

Constraints

* 1 \leq N, Q \leq 500000
* 0 \leq a_i, c < 998244353
* 1 \leq b < 998244353
* 0 \leq l < r \leq N
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N Q
a_0 a_1 ... a_{N - 1}
\textrm{Query}_0
\textrm{Query}_1
:
\textrm{Query}_{Q - 1}


Output

For each query of the latter type, print the answer.

Example

Input

5 7
1 2 3 4 5
1 0 5
0 2 4 100 101
1 0 3
0 1 3 102 103
1 2 5
0 2 5 104 105
1 0 5


Output

15
404
41511
4317767

Solution (in PYTHON3):

Solution:
import sys
input = lambda: sys.stdin.readline().rstrip()

# LazySegmentTree
# Thank "zkou" !
class LazySegmentTree:
  # f(X, X) -> X
  # g(X, M) -> X
  # h(M, M) ->

  def __init__(self, n, p, x_unit, m_unit, f, g, h):
    self.n = n
    self.seg = p*2
    self.x_unit = x_unit
    self.m_unit = m_unit
    self.f = f
    self.g = g
    self.h = h
    for i in range(self.n-1, 0, -1):
      self.seg[i] = self.f(self.seg[i<<1], self.seg[(i<<1)+1])
    self.lazy = [m_unit] * (self.n * 2)

  def update(self, l, r, x):
    l += self.n
    r += self.n
    ll = l // (l & -l)
    rr = r // (r & -r) - 1
    for shift in range(ll.bit_length()-1, 0, -1):
      i = ll >> shift
      self.lazy[i << 1] = self.h(self.lazy[i << 1], self.lazy[i])
      self.lazy[(i << 1)+1] = self.h(self.lazy[(i << 1)+1], self.lazy[i])
      self.seg[i] = self.g(self.seg[i], self.lazy[i])
      self.lazy[i] = self.m_unit
    for shift in range(rr.bit_length()-1, 0, -1):
      i = rr >> shift
      self.lazy[i << 1] = self.h(self.lazy[i << 1],   self.lazy[i])
      self.lazy[(i << 1)+1] = self.h(self.lazy[(i << 1)+1], self.lazy[i])
      self.seg[i] = self.g(self.seg[i], self.lazy[i])
      self.lazy[i] = self.m_unit
    while l < r:
      if l & 1:
        self.lazy[l] = self.h(self.lazy[l], x)
        l += 1
      if r & 1:
        r -= 1
        self.lazy[r] = self.h(self.lazy[r], x)
      l >>= 1
      r >>= 1
    while ll > 1:
      ll >>= 1
      self.seg[ll] = self.f(self.g(self.seg[ll << 1], self.lazy[ll << 1]), self.g(self.seg[(ll << 1)+1], self.lazy[(ll << 1)+1]))
      self.lazy[ll] = self.m_unit
    while rr > 1:
      rr >>= 1
      self.seg[rr] = self.f(self.g(self.seg[rr << 1], self.lazy[rr << 1]), self.g(self.seg[(rr << 1)+1], self.lazy[(rr << 1)+1]))
      self.lazy[rr] = self.m_unit

  def query(self, l, r):
    l += self.n
    r += self.n
    ll = l // (l & -l)
    rr = r // (r & -r) - 1
    for shift in range(ll.bit_length()-1, 0, -1):
      i = ll >> shift
      self.lazy[i << 1] = self.h(self.lazy[i << 1], self.lazy[i])
      self.lazy[(i << 1)+1] = self.h(self.lazy[(i << 1)+1], self.lazy[i])
      self.seg[i] = self.g(self.seg[i], self.lazy[i])
      self.lazy[i] = self.m_unit
    for shift in range(rr.bit_length()-1, 0, -1):
      i = rr >> shift
      self.lazy[i << 1] = self.h(self.lazy[i << 1],   self.lazy[i])
      self.lazy[(i << 1)+1] = self.h(self.lazy[(i << 1)+1], self.lazy[i])
      self.seg[i] = self.g(self.seg[i], self.lazy[i])
      self.lazy[i] = self.m_unit
    ans_l = ans_r = self.x_unit
    while l < r:
      if l & 1:
        ans_l = self.f(ans_l, self.g(self.seg[l], self.lazy[l]))
        l += 1
      if r & 1:
        r -= 1
        ans_r = self.f(self.g(self.seg[r], self.lazy[r]), ans_r)
      l >>= 1
      r >>= 1
    return self.f(ans_l, ans_r)

mod=998244353
mask=(1<<32)-1

n,q=map(int,input().split())
a=[(i<<32)+1 for i in map(int,input().split())]

def f(a,b):
  m=a+b
  return (((m>>32)%mod)<<32)+(m&mask)
def g(a,x):
  a1=a>>32
  a2=a&mask
  x1=x>>32
  x2=x&mask
  return (((a1*x1+a2*x2)%mod)<<32)+a2
def h(x,y):
  x1=x>>32
  x2=x&mask
  y1=y>>32
  y2=y&mask
  a=x1*y1%mod
  b=(x2*y1+y2)%mod
  return (a<<32)+b

seg=LazySegmentTree(n,a,0,(1<<32),f,g,h)

for _ in range(q):
  f,*query=map(int,input().split())
  if f==0:
    l,r,b,c=query
    seg.update(l,r,(b<<32)+c)
  else:
    l,r=query
    print(seg.query(l,r)>>32)