Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.buffer.readline

N, K = map(int, input().split())

MOD = 998244353



I = [tuple(map(int, input().split())) for _ in range(K)]

class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, idx):
        res = 0
        while idx:
            res += self.tree[idx]
            res %= MOD
            idx -= idx & -idx
        return res

    def add(self, idx, x):
        while idx <= self.n:
            self.tree[idx] += x
            self.tree[idx] % MOD
            idx += idx & -idx

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1

class RAQandRSQ():
    def __init__(self, n):
        self.bit1 = BinaryIndexedTree(n)
        self.bit2 = BinaryIndexedTree(n)

    def add(self, lt, rt, x):
        self.bit1.add(lt, -x * (lt - 1))
        self.bit1.add(rt, x * (rt - 1))
        self.bit2.add(lt, x)
        self.bit2.add(rt, -x)

    def sum(self, lt, rt):
        rsum = self.bit2.sum(rt - 1) * (rt - 1) + self.bit1.sum(rt - 1)
        lsum = self.bit2.sum(lt - 1) * (lt - 1) + self.bit1.sum(lt - 1)
        return rsum - lsum

R = RAQandRSQ(N)
R.add(1, 2, 1)

for i in range(1, N):
    s = R.sum(i, i + 1)
    for l, r in I:

        R.add(min(i + l, N + 1), min(i + r + 1, N + 1), s)

print(R.sum(N, N + 1) % MOD)

Fixed submission:
import sys
input = sys.stdin.buffer.readline

N, K = map(int, input().split())

MOD = 998244353

I = [tuple(map(int, input().split())) for _ in range(K)]

class SegmentTreeDual():
    def __init__(self, arr, op=lambda x, y: y if y != -1 else x, ie=-1):
        self.h = (len(arr) - 1).bit_length()
        self.n = 2**self.h
        self.ie = ie
        self.op = op
        self.val = [ie for _ in range(self.n)]
        self.laz = [ie for _ in range(2 * self.n)]
        for i in range(len(arr)):
            self.val[i] = arr[i]

    def propagate(self, k):
        if self.laz[k] == self.ie: return
        if self.n <= k:
            self.val[k - self.n] = self.op(self.val[k - self.n], self.laz[k])
        else:
            self.laz[2 * k] = self.op(self.laz[2 * k], self.laz[k])
            self.laz[2 * k + 1] = self.op(self.laz[2 * k + 1], self.laz[k])
        self.laz[k] = self.ie

    def update(self, lt, rt, x):
        lt += self.n
        rt += self.n
        while rt - lt > 0:
            if lt & 1:
                self.laz[lt] = self.op(self.laz[lt], x)
                self.laz[lt] %= MOD
                lt += 1
            if rt & 1:
                rt -= 1
                self.laz[rt] = self.op(self.laz[rt], x)
                self.laz[rt] %= MOD
            lt >>= 1
            rt >>= 1

    def get(self, idx):
        res = self.val[idx]
        idx += self.n
        while idx:
            res = self.op(res, self.laz[idx])
            res %= MOD
            idx >>= 1
        return res

from operator import add

arr = [0] * N
arr[0] = 1

S = SegmentTreeDual(arr, add, 0)

for i in range(N - 1):
    s = S.get(i)
    for l, r in I:
        S.update(min(i + l, N), min(i + r + 1, N), s)

print(S.get(N - 1) % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.buffer.readline

N, K = map(int, input().split())

MOD = 998244353



I = [tuple(map(int, input().split())) for _ in range(K)]

class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, idx):
        res = 0
        while idx:
            res += self.tree[idx]
            res %= MOD
            idx -= idx & -idx
        return res

    def add(self, idx, x):
        while idx <= self.n:
            self.tree[idx] += x
            self.tree[idx] % MOD
            idx += idx & -idx

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1

class RAQandRSQ():
    def __init__(self, n):
        self.bit1 = BinaryIndexedTree(n)
        self.bit2 = BinaryIndexedTree(n)

    def add(self, lt, rt, x):
        self.bit1.add(lt, -x * (lt - 1))
        self.bit1.add(rt, x * (rt - 1))
        self.bit2.add(lt, x)
        self.bit2.add(rt, -x)

    def sum(self, lt, rt):
        rsum = self.bit2.sum(rt - 1) * (rt - 1) + self.bit1.sum(rt - 1)
        lsum = self.bit2.sum(lt - 1) * (lt - 1) + self.bit1.sum(lt - 1)
        return rsum - lsum

R = RAQandRSQ(N)
R.add(1, 2, 1)

for i in range(1, N):
    s = R.sum(i, i + 1)
    for l, r in I:
        R.add(i + l, i + r + 1, s)

print(R.sum(N, N + 1) % MOD)

Fixed submission:
import sys
input = sys.stdin.buffer.readline

N, K = map(int, input().split())

MOD = 998244353

I = [tuple(map(int, input().split())) for _ in range(K)]

class SegmentTreeDual():
    def __init__(self, arr, op=lambda x, y: y if y != -1 else x, ie=-1):
        self.h = (len(arr) - 1).bit_length()
        self.n = 2**self.h
        self.ie = ie
        self.op = op
        self.val = [ie for _ in range(self.n)]
        self.laz = [ie for _ in range(2 * self.n)]
        for i in range(len(arr)):
            self.val[i] = arr[i]

    def propagate(self, k):
        if self.laz[k] == self.ie: return
        if self.n <= k:
            self.val[k - self.n] = self.op(self.val[k - self.n], self.laz[k])
        else:
            self.laz[2 * k] = self.op(self.laz[2 * k], self.laz[k])
            self.laz[2 * k + 1] = self.op(self.laz[2 * k + 1], self.laz[k])
        self.laz[k] = self.ie

    def update(self, lt, rt, x):
        lt += self.n
        rt += self.n
        while rt - lt > 0:
            if lt & 1:
                self.laz[lt] = self.op(self.laz[lt], x)
                self.laz[lt] %= MOD
                lt += 1
            if rt & 1:
                rt -= 1
                self.laz[rt] = self.op(self.laz[rt], x)
                self.laz[rt] %= MOD
            lt >>= 1
            rt >>= 1

    def get(self, idx):
        res = self.val[idx]
        idx += self.n
        while idx:
            res = self.op(res, self.laz[idx])
            res %= MOD
            idx >>= 1
        return res

from operator import add

arr = [0] * N
arr[0] = 1

S = SegmentTreeDual(arr, add, 0)

for i in range(N - 1):
    s = S.get(i)
    for l, r in I:
        S.update(min(i + l, N), min(i + r + 1, N), s)

print(S.get(N - 1) % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
N, K = map(int, input().split())

MOD = 998244353

I = [tuple(map(int, input().split())) for _ in range(K)]

class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, idx):
        res = 0
        while idx:
            res += self.tree[idx]
            res %= MOD
            idx -= idx & -idx
        return res

    def add(self, idx, x):
        while idx <= self.n:
            self.tree[idx] += x
            self.tree[idx] % MOD
            idx += idx & -idx

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1

class RAQandRSQ():
    def __init__(self, n):
        self.bit1 = BinaryIndexedTree(n)
        self.bit2 = BinaryIndexedTree(n)

    def add(self, lt, rt, x):
        self.bit1.add(lt, -x * (lt - 1))
        self.bit1.add(rt, x * (rt - 1))
        self.bit2.add(lt, x)
        self.bit2.add(rt, -x)

    def sum(self, lt, rt):
        rsum = self.bit2.sum(rt - 1) * (rt - 1) + self.bit1.sum(rt - 1)
        lsum = self.bit2.sum(lt - 1) * (lt - 1) + self.bit1.sum(lt - 1)
        return rsum - lsum

R = RAQandRSQ(N)
R.add(1, 2, 1)

for i in range(1, N):
    s = R.sum(i, i + 1)
    for l, r in I:
        R.add(i + l, i + r + 1, s)

print(R.sum(N, N + 1) % MOD)

Fixed submission:
import sys
input = sys.stdin.buffer.readline

N, K = map(int, input().split())

MOD = 998244353

I = [tuple(map(int, input().split())) for _ in range(K)]

class SegmentTreeDual():
    def __init__(self, arr, op=lambda x, y: y if y != -1 else x, ie=-1):
        self.h = (len(arr) - 1).bit_length()
        self.n = 2**self.h
        self.ie = ie
        self.op = op
        self.val = [ie for _ in range(self.n)]
        self.laz = [ie for _ in range(2 * self.n)]
        for i in range(len(arr)):
            self.val[i] = arr[i]

    def propagate(self, k):
        if self.laz[k] == self.ie: return
        if self.n <= k:
            self.val[k - self.n] = self.op(self.val[k - self.n], self.laz[k])
        else:
            self.laz[2 * k] = self.op(self.laz[2 * k], self.laz[k])
            self.laz[2 * k + 1] = self.op(self.laz[2 * k + 1], self.laz[k])
        self.laz[k] = self.ie

    def update(self, lt, rt, x):
        lt += self.n
        rt += self.n
        while rt - lt > 0:
            if lt & 1:
                self.laz[lt] = self.op(self.laz[lt], x)
                self.laz[lt] %= MOD
                lt += 1
            if rt & 1:
                rt -= 1
                self.laz[rt] = self.op(self.laz[rt], x)
                self.laz[rt] %= MOD
            lt >>= 1
            rt >>= 1

    def get(self, idx):
        res = self.val[idx]
        idx += self.n
        while idx:
            res = self.op(res, self.laz[idx])
            res %= MOD
            idx >>= 1
        return res

from operator import add

arr = [0] * N
arr[0] = 1

S = SegmentTreeDual(arr, add, 0)

for i in range(N - 1):
    s = S.get(i)
    for l, r in I:
        S.update(min(i + l, N), min(i + r + 1, N), s)

print(S.get(N - 1) % MOD)