Problem:


Score : 100 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

15
404
41511
4317767



Sample 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


Sample output:
15
404
41511
4317767

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


### 遅延評価セグメント木
class LazySegmentTree:
    def __init__(self, n, a=None):
        """初期化
        num : n以上の最小の2のべき乗
        """
        num = 1
        while num<=n:
            num *= 2
        self.num = num
        self.seg = [ninf] * (2*self.num-1)
        self.lazy = [f0] * (2*self.num-1)
        self.ls = [0]*(2*self.num-1)
        self.rs = [0]*(2*self.num-1)
        self.ls[0] = 0
        self.rs[0] = self.num
        for i in range(self.num-1):
            self.ls[2*i+1] = self.ls[i]
            self.rs[2*i+1] = (self.ls[i] + self.rs[i])//2
            self.ls[2*i+2] = (self.ls[i] + self.rs[i])//2
            self.rs[2*i+2] = self.rs[i]
        if a is not None:
            # O(n)で初期化
            assert len(a)==n
            for i in range(n):
                self.seg[num-1+i] = a[i]
            for k in range(num-2, -1, -1):
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def eval(self, k):
        if self.lazy[k]==f0:
            return 
        if k<self.num-1:
            self.lazy[k*2+1] = composition(self.lazy[k], self.lazy[k*2+1])
            self.lazy[k*2+2] = composition(self.lazy[k], self.lazy[k*2+2])
        self.seg[k] = mapping(self.lazy[k], self.seg[k])
        self.lazy[k] = f0
    def eval_all(self):
        for i in range(2*self.num-1):
            self.eval(i)
    def update(self,a,b,x=None,f=None):
        """A[a]...A[b-1]をxに更新する
        """
        if f is None:
            # 更新クエリ
            f = lambda y: x
        k = 0
        q = [k] # k>=0なら行きがけ順
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            if k>=0:
                self.eval(k)
                if r<=a or b<=l:
                    continue
                elif a<=l and r<=b:
                    self.lazy[k] = composition(f, self.lazy[k])
                    self.eval(k)
                else:
                    q.append(~k)
                    q.append(2*k+1)
                    q.append(2*k+2)
            else:
                k = ~k
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def query(self,a,b):
        k = 0
        l = 0
        r = self.num
        q = [k]
        ans = ninf
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            self.eval(k)
            if r<=a or b<=l:
                continue
            elif a<=l and r<=b:
                ans = op(ans, self.seg[k])
            else:
                q.append(2*k+2)
                q.append(2*k+1)
#             print(q, ans, l,r,a,b, self.seg[k])
        return ans


n,q = list(map(int, input().split()))
a = list(map(int, input().split()))
# ninf = -10**9
# op = max
# mapping = lambda f,x: f(x)
# composition = lambda f1, f2: f1 if f1 is not None else f2
M = 998244353
ninf = 0
B = 30
f0 = 1<<B
def op(x,y):
    x0,x1 = x>>B, x%(1<<B)
    y0,y1 = y>>B, y%(1<<B)
    return (((x0+y0)%M)<<B) + x1+y1
def mapping(f,x):
    x0,x1 = x>>B, x%(1<<B)
    f0,f1 = f>>B, f%(1<<B)
    return (((f0*x0 + f1*x1)%M)<<B) + x1
def composition(f,g):
    g0,g1 = g>>B, g%(1<<B)
    f0,f1 = f>>B, f%(1<<B)
    return (((f0*g0)%M)<<B) + (g1*f0 + f1)%M
# op = lambda x,y: ((x[0]+y[0])%M, (x[1]+y[1]))
# mapping = lambda f,x: ((f[0]*x[0] + f[1]*x[1])%M, x[1])
# composition = lambda f1, f2: ((f1[0]*f2[0])%M, (f2[1]*f1[0]+f1[1])%M)
# f0 = (1,0)
sg = LazySegmentTree(n, [((item<<B)+1) for item in a])
ans = []
for _ in range(q):
    t = tuple(map(int, input().split()))
    if t[0]==0:
        _, l,r,b,c = t
        sg.update(l,r,f=((b<<B)+c))
    else:
        _,s,t = t
        ans.append(sg.query(s,t)>>B)
        
write("\n".join(map(str, ans)))

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


### 遅延評価セグメント木
class LazySegmentTree:
    def __init__(self, n, a=None):
        """初期化
        num : n以上の最小の2のべき乗
        """
        num = 1
        while num<=n:
            num *= 2
        self.num = num
        self.seg = [ninf] * (2*self.num-1)
        self.lazy = [f0] * (2*self.num-1)
        self.ls = [0]*(2*self.num-1)
        self.rs = [0]*(2*self.num-1)
        self.ls[0] = 0
        self.rs[0] = self.num
        for i in range(self.num-1):
            self.ls[2*i+1] = self.ls[i]
            self.rs[2*i+1] = (self.ls[i] + self.rs[i])//2
            self.ls[2*i+2] = (self.ls[i] + self.rs[i])//2
            self.rs[2*i+2] = self.rs[i]
        if a is not None:
            # O(n)で初期化
            assert len(a)==n
            for i in range(n):
                self.seg[num-1+i] = a[i]
            for k in range(num-2, -1, -1):
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def eval(self, k):
        if self.lazy[k]==f0:
            return 
        if k<self.num-1:
            self.lazy[k*2+1] = composition(self.lazy[k], self.lazy[k*2+1])
            self.lazy[k*2+2] = composition(self.lazy[k], self.lazy[k*2+2])
        self.seg[k] = mapping(self.lazy[k], self.seg[k])
        self.lazy[k] = f0
    def eval_all(self):
        for i in range(2*self.num-1):
            self.eval(i)
    def update(self,a,b,x=None,f=None):
        """A[a]...A[b-1]をxに更新する
        """
        if f is None:
            # 更新クエリ
            f = lambda y: x
        k = 0
        q = [k] # k>=0なら行きがけ順
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            if k>=0:
                self.eval(k)
                if r<=a or b<=l:
                    continue
                elif a<=l and r<=b:
                    self.lazy[k] = composition(f, self.lazy[k])
                    self.eval(k)
                else:
                    q.append(~k)
                    q.append(2*k+1)
                    q.append(2*k+2)
            else:
                k = ~k
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def query(self,a,b):
        k = 0
        l = 0
        r = self.num
        q = [k]
        ans = ninf
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            self.eval(k)
            if r<=a or b<=l:
                continue
            elif a<=l and r<=b:
                ans = op(ans, self.seg[k])
            else:
                q.append(2*k+2)
                q.append(2*k+1)
#             print(q, ans, l,r,a,b, self.seg[k])
        return ans


n,q = list(map(int, input().split()))
a = list(map(int, input().split()))
# ninf = -10**9
# op = max
# mapping = lambda f,x: f(x)
# composition = lambda f1, f2: f1 if f1 is not None else f2
M = 998244353
ninf = 0
f0 = 1<<32
def op(x,y):
    x0,x1 = x>>32, x%(1<<32)
    y0,y1 = y>>32, y%(1<<32)
    return (((x0+y0)%M)<<32) + x1+y1
def mapping(f,x):
    x0,x1 = x>>32, x%(1<<32)
    f0,f1 = f>>32, f%(1<<32)
    return (((f0*x0 + f1*x1)%M)<<32) + x1
def composition(f,g):
    g0,g1 = g>>32, g%(1<<32)
    f0,f1 = f>>32, f%(1<<32)
    return (((f0*g0)%M)<<32) + (g1*f0 + f1)%M
# op = lambda x,y: ((x[0]+y[0])%M, (x[1]+y[1]))
# mapping = lambda f,x: ((f[0]*x[0] + f[1]*x[1])%M, x[1])
# composition = lambda f1, f2: ((f1[0]*f2[0])%M, (f2[1]*f1[0]+f1[1])%M)
# f0 = (1,0)
sg = LazySegmentTree(n, [((item<<32)+1) for item in a])
ans = []
for _ in range(q):
    t = tuple(map(int, input().split()))
    if t[0]==0:
        _, l,r,b,c = t
        sg.update(l,r,f=((b<<32)+c))
    else:
        _,s,t = t
        ans.append(sg.query(s,t)>>32)
        
write("\n".join(map(str, ans)))

Submission status: Accepted

Solution code:
mod = 998244353
eps = 10**-9


def main():
    import sys
    input = sys.stdin.buffer.readline

    def op(a, b):
        return (a + b) % mod

    e = 0

    mask = 2**32 - 1
    def mapping(a, x, seg_len):
        b = x >> 32
        c = x & mask
        return ((a * b)%mod + (c * seg_len)%mod)%mod

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

    id = 1 << 32

    class LazySegTree:
        # Range update query
        def __init__(self, A, op=op, e=e, mapping=mapping, composition=composition, id=id, initialize=True):
            self.N = len(A)
            self.LV = (self.N - 1).bit_length()
            self.N0 = 1 << self.LV
            self.op = op
            self.e = e
            self.mapping = mapping
            self.composition = composition
            self.id = id
            if initialize:
                self.data = [self.e] * self.N0 + A + [self.e] * (self.N0 - self.N)
                for i in range(self.N0 - 1, 0, -1):
                    self.data[i] = op(self.data[i * 2], self.data[i * 2 + 1])
            else:
                self.data = [self.e] * (self.N0 * 2)
            self.lazy = [id] * (self.N0 * 2)

        def _ascend(self, i):
            for _ in range(i.bit_length() - 1):
                i >>= 1
                self.data[i] = self.op(self.data[i * 2], self.data[i * 2 + 1])

        def _descend(self, idx):
            lv = idx.bit_length()
            seg_len = 1 << self.LV
            for j in range(lv - 1, 0, -1):
                seg_len >>= 1
                i = idx >> j
                x = self.lazy[i]
                if x == self.id:
                    continue
                self.lazy[i * 2] = self.composition(self.lazy[i * 2], x)
                self.lazy[i * 2 + 1] = self.composition(self.lazy[i * 2 + 1], x)
                self.lazy[i] = self.id
                self.data[i * 2] = self.mapping(self.data[i * 2], x, seg_len)
                self.data[i * 2 + 1] = self.mapping(self.data[i * 2 + 1], x, seg_len)

        # open interval [l, r)
        def apply(self, l, r, x):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            l_ori = l
            r_ori = r
            seg_len = 1
            while l < r:
                if l & 1:
                    self.data[l] = self.mapping(self.data[l], x, seg_len)
                    self.lazy[l] = self.composition(self.lazy[l], x)
                    l += 1
                if r & 1:
                    r -= 1
                    self.data[r] = self.mapping(self.data[r], x, seg_len)
                    self.lazy[r] = self.composition(self.lazy[r], x)
                l >>= 1
                r >>= 1
                seg_len <<= 1
            self._ascend(l_ori // (l_ori & -l_ori))
            self._ascend(r_ori // (r_ori & -r_ori) - 1)

        # open interval [l, r)
        def query(self, l, r):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            ret = self.e
            while l < r:
                if l & 1:
                    ret = self.op(ret, self.data[l])
                    l += 1
                if r & 1:
                    ret = self.op(self.data[r - 1], ret)
                    r -= 1
                l >>= 1
                r >>= 1
            return ret

    N, Q = map(int, input().split())
    A = list(map(int, input().split()))
    ST = LazySegTree(A)
    for _ in range(Q):
        q = list(map(int, input().split()))
        if q[0] == 0:
            l, r, b, c = q[1:]
            l += 1
            r += 1
            ST.apply(l, r, (b << 32) + c)
        else:
            l, r = q[1:]
            l += 1
            r += 1
            print(ST.query(l, r))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
mod = 998244353
eps = 10**-9


def main():
    import sys
    input = sys.stdin.buffer.readline

    def op(a, b):
        return (a + b) % mod

    e = 0

    mask = 2**32 - 1
    def mapping(a, x, seg_len):
        b = x >> 32
        c = x & mask
        return ((a * b)%mod + (c * seg_len)%mod)%mod

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

    id = 1 << 32

    class LazySegTree:
        # Range update query
        def __init__(self, A, op=op, e=e, mapping=mapping, composition=composition, id=id, initialize=True):
            self.N = len(A)
            self.LV = (self.N - 1).bit_length()
            self.N0 = 1 << self.LV
            self.op = op
            self.e = e
            self.mapping = mapping
            self.composition = composition
            self.id = id
            if initialize:
                self.data = [self.e] * self.N0 + A + [self.e] * (self.N0 - self.N)
                for i in range(self.N0 - 1, 0, -1):
                    self.data[i] = op(self.data[i * 2], self.data[i * 2 + 1])
            else:
                self.data = [self.e] * (self.N0 * 2)
            self.lazy = [id] * (self.N0 * 2)

        def _ascend(self, i):
            for _ in range(i.bit_length() - 1):
                i >>= 1
                self.data[i] = self.op(self.data[i * 2], self.data[i * 2 + 1])

        def _descend(self, idx):
            lv = idx.bit_length()
            for j in range(lv - 1, 0, -1):
                i = idx >> j
                x = self.lazy[i]
                if x == self.id:
                    continue
                self.lazy[i * 2] = self.composition(self.lazy[i * 2], x)
                self.lazy[i * 2 + 1] = self.composition(self.lazy[i * 2 + 1], x)
                self.lazy[i] = self.id
                self.data[i * 2] = self.mapping(self.data[i * 2], x, 1 << (self.LV + j - lv))
                self.data[i * 2 + 1] = self.mapping(self.data[i * 2 + 1], x, 1 << (self.LV + j - lv))

        # open interval [l, r)
        def apply(self, l, r, x):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            l_ori = l
            r_ori = r
            seg_len = 1
            while l < r:
                if l & 1:
                    self.data[l] = self.mapping(self.data[l], x, seg_len)
                    self.lazy[l] = self.composition(self.lazy[l], x)
                    l += 1
                if r & 1:
                    r -= 1
                    self.data[r] = self.mapping(self.data[r], x, seg_len)
                    self.lazy[r] = self.composition(self.lazy[r], x)
                l >>= 1
                r >>= 1
                seg_len <<= 1
            self._ascend(l_ori // (l_ori & -l_ori))
            self._ascend(r_ori // (r_ori & -r_ori) - 1)

        # open interval [l, r)
        def query(self, l, r):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            ret = self.e
            while l < r:
                if l & 1:
                    ret = self.op(ret, self.data[l])
                    l += 1
                if r & 1:
                    ret = self.op(self.data[r - 1], ret)
                    r -= 1
                l >>= 1
                r >>= 1
            return ret

    N, Q = map(int, input().split())
    A = list(map(int, input().split()))
    ST = LazySegTree(A)
    for _ in range(Q):
        q = list(map(int, input().split()))
        if q[0] == 0:
            l, r, b, c = q[1:]
            l += 1
            r += 1
            ST.apply(l, r, (b << 32) + c)
        else:
            l, r = q[1:]
            l += 1
            r += 1
            print(ST.query(l, r))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
class LazySegmentTree():
    def __init__(self, n, op, e, mapping, composition, id):
        self.n = n
        self.op = op
        self.e = e
        self.mapping = mapping
        self.composition = composition
        self.id = id
        self.log = (n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e] * (2 * self.size)
        self.lz = [id] * (self.size)

    def update(self, k):
        self.d[k] = self.op(self.d[2 * k], self.d[2 * k + 1])

    def all_apply(self, k, f):
        self.d[k] = self.mapping(f, self.d[k])
        if k < self.size: self.lz[k] = self.composition(f, self.lz[k])

    def push(self, k):
        self.all_apply(2 * k, self.lz[k])
        self.all_apply(2 * k + 1, self.lz[k])
        self.lz[k] = self.id

    def build(self, arr):
        #assert len(arr) == self.n
        for i in range(self.n): self.d[self.size + i] = arr[i]
        for i in range(1, self.size)[::-1]: self.update(i)

    def set(self, p, x):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1)[::-1]: self.push(p >> i)
        self.d[p] = x
        for i in range(1, self.log + 1): self.update(p >> i)

    def get(self, p):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1): self.push(p >> i)
        return self.d[p]

    def prod(self, l, r):
        #assert 0 <= l <= r <= self.n
        if l == r: return self.e
        l += self.size
        r += self.size
        for i in range(1, self.log + 1)[::-1]:
            if ((l >> i) << i) != l: self.push(l >> i)
            if ((r >> i) << i) != r: self.push(r >> i)
        sml = smr = self.e
        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self):
        return self.d[1]

    def apply(self, p, f):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1)[::-1]: self.push(p >> i)
        self.d[p] = self.mapping(f, self.d[p])
        for i in range(1, self.log + 1): self.update(p >> i)

    def range_apply(self, l, r, f):
        #assert 0 <= l <= r <= self.n
        if l == r: return
        l += self.size
        r += self.size
        for i in range(1, self.log + 1)[::-1]:
            if ((l >> i) << i) != l: self.push(l >> i)
            if ((r >> i) << i) != r: self.push((r - 1) >> i)
        l2 = l
        r2 = r
        while l < r:
            if l & 1:
                self.all_apply(l, f)
                l += 1
            if r & 1:
                r -= 1
                self.all_apply(r, f)
            l >>= 1
            r >>= 1
        l = l2
        r = r2
        for i in range(1, self.log + 1):
            if ((l >> i) << i) != l: self.update(l >> i)
            if ((r >> i) << i) != r: self.update((r - 1) >> i)

    def max_right(self, l, g):
        #assert 0 <= l <= self.n
        #assert g(self.e)
        if l == self.n: return self.n
        l += self.size
        for i in range(1, self.log + 1)[::-1]: self.push(l >> i)
        sm = self.e
        while True:
            while l % 2 == 0: l >>= 1
            if not g(self.op(sm, self.d[l])):
                while l < self.size:
                    self.push(l)
                    l = 2 * l
                    if g(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l: return self.n

    def min_left(self, r, g):
        #assert 0 <= r <= self.n
        #assert g(self.e)
        if r == 0: return 0
        r += self.size
        for i in range(1, self.log + 1)[::-1]: self.push((r - 1) >> i)
        sm = self.e
        while True:
            r -= 1
            while r > 1 and r % 2: r >>= 1
            if not g(self.op(self.d[r], sm)):
                while r < self.size:
                    self.push(r)
                    r = 2 * r + 1
                    if g(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r: return 0

import sys
input = sys.stdin.buffer.readline

MOD = 998244353

N, Q = map(int, input().split())
A = tuple((int(a) << 32) + 1 for a in input().split())

def op(a, b):
    a1, a2 = a >> 32, a % (1 << 32)
    b1, b2 = b >> 32, b % (1 << 32)
    c1 = (a1 + b1) % MOD
    c2 = (a2 + b2) % MOD
    return (c1 << 32) + c2

def mapping(x, a):
    x1, x2 = x >> 32, x % (1 << 32)
    a1, a2 = a >> 32, a % (1 << 32)
    c1 = (a1 * x1 + a2 * x2) % MOD
    return (c1 << 32) + a2

def composition(x, y):
    x1, x2 = x >> 32, x % (1 << 32)
    y1, y2 = y >> 32, y % (1 << 32)
    z1 = (x1 * y1) % MOD
    z2 = (x1 * y2 + x2) % MOD
    return (z1 << 32) + z2

lst = LazySegmentTree(N, op, 0, mapping, composition, 1 << 32)
lst.build(A)

res = []

for _ in range(Q):
    t, *q = tuple(map(int, input().split()))
    if t == 0:
        l, r, b, c = q
        lst.range_apply(l, r, (b << 32) + c)
    else:
        l, r = q
        res.append(lst.prod(l, r) >> 32)

print('\n'.join(map(str, res)))

Submission status: Accepted

Solution code:
class LazySegmentTree():
    def __init__(self, n, op, e, mapping, composition, id):
        self.n = n
        self.op = op
        self.e = e
        self.mapping = mapping
        self.composition = composition
        self.id = id
        self.log = (n - 1).bit_length()
        self.size = 1 << self.log
        self.d = [e] * (2 * self.size)
        self.lz = [id] * (self.size)

    def update(self, k):
        self.d[k] = self.op(self.d[2 * k], self.d[2 * k + 1])

    def all_apply(self, k, f):
        self.d[k] = self.mapping(f, self.d[k])
        if k < self.size:
            self.lz[k] = self.composition(f, self.lz[k])

    def push(self, k):
        self.all_apply(2 * k, self.lz[k])
        self.all_apply(2 * k + 1, self.lz[k])
        self.lz[k] = self.id

    def build(self, arr):
        #assert len(arr) == self.n
        for i in range(self.n):
            self.d[self.size + i] = arr[i]
        for i in range(1, self.size)[::-1]:
            self.update(i)

    def set(self, p, x):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1)[::-1]:
            self.push(p >> i)
        self.d[p] = x
        for i in range(1, self.log + 1):
            self.update(p >> i)

    def get(self, p):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1):
            self.push(p >> i)
        return self.d[p]

    def prod(self, l, r):
        #assert 0 <= l <= r <= self.n
        if l == r: return self.e
        l += self.size
        r += self.size
        for i in range(1, self.log + 1)[::-1]:
            if ((l >> i) << i) != l: self.push(l >> i)
            if ((r >> i) << i) != r: self.push(r >> i)
        sml = smr = self.e
        while l < r:
            if l & 1:
                sml = self.op(sml, self.d[l])
                l += 1
            if r & 1:
                r -= 1
                smr = self.op(self.d[r], smr)
            l >>= 1
            r >>= 1
        return self.op(sml, smr)

    def all_prod(self):
        return self.d[1]

    def apply(self, p, f):
        #assert 0 <= p < self.n
        p += self.size
        for i in range(1, self.log + 1)[::-1]:
            self.push(p >> i)
        self.d[p] = self.mapping(f, self.d[p])
        for i in range(1, self.log + 1):
            self.update(p >> i)

    def range_apply(self, l, r, f):
        #assert 0 <= l <= r <= self.n
        if l == r: return
        l += self.size
        r += self.size
        for i in range(1, self.log + 1)[::-1]:
            if ((l >> i) << i) != l: self.push(l >> i)
            if ((r >> i) << i) != r: self.push((r - 1) >> i)
        l2 = l
        r2 = r
        while l < r:
            if l & 1:
                self.all_apply(l, f)
                l += 1
            if r & 1:
                r -= 1
                self.all_apply(r, f)
            l >>= 1
            r >>= 1
        l = l2
        r = r2
        for i in range(1, self.log + 1):
            if ((l >> i) << i) != l: self.update(l >> i)
            if ((r >> i) << i) != r: self.update((r - 1) >> i)

    def max_right(self, l, g):
        #assert 0 <= l <= self.n
        #assert g(self.e)
        if l == self.n: return self.n
        l += self.size
        for i in range(1, self.log + 1)[::-1]:
            self.push(l >> i)
        sm = self.e
        while True:
            while l % 2 == 0: l >>= 1
            if not g(self.op(sm, self.d[l])):
                while l < self.size:
                    self.push(l)
                    l = 2 * l
                    if g(self.op(sm, self.d[l])):
                        sm = self.op(sm, self.d[l])
                        l += 1
                return l - self.size
            sm = self.op(sm, self.d[l])
            l += 1
            if (l & -l) == l: return self.n

    def min_left(self, r, g):
        #assert 0 <= r <= self.n
        #assert g(self.e)
        if r == 0: return 0
        r += self.size
        for i in range(1, self.log + 1)[::-1]:
            self.push((r - 1) >> i)
        sm = self.e
        while True:
            r -= 1
            while r > 1 and r % 2: r >>= 1
            if not g(self.op(self.d[r], sm)):
                while r < self.size:
                    self.push(r)
                    r = 2 * r + 1
                    if g(self.op(self.d[r], sm)):
                        sm = self.op(self.d[r], sm)
                        r -= 1
                return r + 1 - self.size
            sm = self.op(self.d[r], sm)
            if (r & -r) == r: return 0

import sys
input = sys.stdin.buffer.readline

MOD = 998244353

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

def op(a, b):
    a1, a2 = a >> 32, a % (1 << 32)
    b1, b2 = b >> 32, b % (1 << 32)
    c1 = (a1 + b1) % MOD
    c2 = (a2 + b2) % MOD
    return (c1 << 32) + c2

def mapping(x, a):
    x1, x2 = x >> 32, x % (1 << 32)
    a1, a2 = a >> 32, a % (1 << 32)
    c1 = (a1 * x1 + a2 * x2) % MOD
    c2 = a2
    return (c1 << 32) + c2

def composition(x, y):
    x1, x2 = x >> 32, x % (1 << 32)
    y1, y2 = y >> 32, y % (1 << 32)
    z1 = (x1 * y1) % MOD
    z2 = (x1 * y2 + x2) % MOD
    return (z1 << 32) + z2

lst = LazySegmentTree(N, op, 0, mapping, composition, 1 << 32)
lst.build(A)

res = []

for _ in range(Q):
    t, *q = tuple(map(int, input().split()))
    if t == 0:
        l, r, b, c = q
        lst.range_apply(l, r, (b << 32) + c)
    else:
        l, r = q
        res.append(str(lst.prod(l, r) >> 32))

print('\n'.join(res))