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:
class LazySegmentTree():
    def __init__(self,n,init,merge,merge_unit,operate,merge_operate,operate_unit):
        self.merge=merge
        self.merge_unit=merge_unit
        self.operate=operate
        self.merge_operate=merge_operate
        self.operate_unit=operate_unit

        self.n=(n-1).bit_length()
        self.num = 1<<self.n
        self.data=[merge_unit for i in range(1<<(self.n+1))]
        self.lazy=[operate_unit for i in range(1<<(self.n+1))]
        if init:
            for i in range(n):
                self.data[2**self.n+i]=init[i]
            for i in range(2**self.n-1,0,-1):
                self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])

    def propagate(self,v):
        ope = self.lazy[v]
        if ope == self.operate_unit:
            return
        self.lazy[v]=self.operate_unit
        self.data[2*v]=self.operate(self.data[2*v],ope)
        self.data[2*v+1]=self.operate(self.data[2*v+1],ope)
        self.lazy[2*v]=self.merge_operate(self.lazy[2*v],ope)
        self.lazy[2*v+1]=self.merge_operate(self.lazy[2*v+1],ope)

    def propagate_above(self,i):
        m=i.bit_length()-1
        for bit in range(m,0,-1):
            v=i>>bit
            self.propagate(v)

    def remerge_above(self,i):
        while i:
            i>>=1
            self.data[i]=self.operate(self.merge(self.data[2*i],self.data[2*i+1]),self.lazy[i])

    def update(self,l,r,x):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        while l<r:
            if l&1:
                self.data[l]=self.operate(self.data[l],x)
                self.lazy[l]=self.merge_operate(self.lazy[l],x)
                l+=1
            if r&1:
                self.data[r-1]=self.operate(self.data[r-1],x)
                self.lazy[r-1]=self.merge_operate(self.lazy[r-1],x)
            l>>=1
            r>>=1
        self.remerge_above(l0)
        self.remerge_above(r0)

    def query(self,l,r):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        res=self.merge_unit
        while l<r:
            if l&1:
                res=self.merge(res,self.data[l])
                l+=1
            if r&1:
                res=self.merge(res,self.data[r-1])
            l>>=1
            r>>=1
        return res>>32

import sys

input = sys.stdin.buffer.readline

mod = 998244353
mask = 2**32 - 1

def merge(x,y):
    s = ((x>>32) + (y>>32)) % mod
    num = (x&mask) + (y&mask)
    return (s<<32) + num

merge_unit = 0

def operate(x,ope):
    s,num = x>>32,x&mask
    b,c = ope>>32,ope&mask
    s = (b*s + c*num) % mod
    return (s<<32)+num

def merge_operate(x,y):
    b1,c1 = x>>32,x&mask
    b2,c2 = y>>32,y&mask
    return (((b1*b2)%mod)<<32)+((b2*c1+c2)%mod)

operate_unit = 1<<32

N,Q = map(int,input().split())
a = list(map(int,input().split()))
a = [(a[i]<<32)+1 for i in range(N)]

LST = LazySegmentTree(N,a,merge,merge_unit,operate,merge_operate,operate_unit)

for _ in range(Q):
    query = list(map(int,input().split()))
    if query[0] == 0:
        gomi,l,r,b,c = query
        LST.update(l,r,(b<<32)+c)
    else:
        gomi,l,r = query
        print(LST.query(l,r))