Buggy python submission (verdict: Time Limit Exceeded):
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    

def main():
    N, K = MI()
    L = [LI() for i in range(K)]
    D = [0] * N
    D[0] = 1
    D[1] = -1
    num = 0
    for index in range(N):
        num += D[index]
        for l, r in L:
            if index + r + 1 <= N-1:
                D[index+l] += num
                D[index+r+1] -= num
            elif index+l <= N-1:
                D[index+l] += num
                
    print(num % 998244353)
    
if __name__ == "__main__":
    main()

Fixed submission:
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    

def main():
    N, K = MI()
    L = [LI() for i in range(K)]
    D = [0] * N
    D[0] = 1
    D[1] = -1
    num = 0
    mod = 998244353
    for index in range(N):
        num += D[index] % mod
        for l, r in L:
            if index + r + 1 <= N-1:
                D[index+l] += num
                D[index+r+1] -= num
            elif index+l <= N-1:
                D[index+l] += num
                
    print(num % mod)
    
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    
class BIT():
    # 作りたい要素数nで初期化
    # 使用するインスタンス変数の初期化
    def __init__(self, n):
        self.n = n
        self.bit = [0] * (n+1)

    #bit_indexにxをO(log(n))で加算する
    def add(self,i,x):
        #if(i<=0 or i>n):return iに0以下の数字は代入しない
        while i <= self.n:
            self.bit[i] += x
            i += (i & -i)
    #bit_1 + bit_2 + …  + bit_n をO(log(n))で求める
    def sum(self,i):
        s = 0
        #iに0以下の数字は代入しない。
        while i > 0:
            s+=self.bit[i]
            i -= (i & -i)
        return s
    
    def rangesum(self,i,k):
        return self.sum(k) - self.sum(i)
    #a_1 + a_2 + … + a_i >= x となるような最小のiを求める(a_k >= 0)
    #xが0以下の場合は該当するものなし→0を返す
    def lower_bound(self,x):
        if x <= 0:
            return 0
        else:
            i = 0
            r = 1
            #最大としてありうる区間の長さを取得する
            #n以下の最小の二乗のべき(BITで管理する数列の区間で最大のもの)を求める
            while(r<self.n):
                r=r<<1
            len = r
            while len > 0:
                if(i+len<self.n and self.bit[i+len]<x):
                    x-=self.bit[i+len]
                    i+=len
                len = len >> 1
            return i+1

def main():
    N, K = MI()
    L = [LI() for i in range(K)]
    Bit = BIT(N)
    Bit.add(1,1)
    Bit.add(2,-1)
    for index in range(1,N+1):
        num = Bit.sum(index)
        for l, r in L:
            if index + r + 1 <= N:
                Bit.add(index+l, num)
                Bit.add(index+r+1, - num)
            elif index+l <= N:
                Bit.add(index+l, num)
                
    print(Bit.sum(N) % 998244353)
                
    
    
if __name__ == "__main__":
    main()

Fixed submission:
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    

def main():
    N, K = MI()
    L = [LI() for i in range(K)]
    D = [0] * N
    D[0] = 1
    D[1] = -1
    num = 0
    mod = 998244353
    for index in range(N):
        num += D[index] % mod
        for l, r in L:
            if index + r + 1 <= N-1:
                D[index+l] += num
                D[index+r+1] -= num
            elif index+l <= N-1:
                D[index+l] += num
                
    print(num % mod)
    
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    
    
def main():
    N, K = MI()
    D = [0] * N
    L = [LI() for i in range(K)]
    D[0] = 1
    for index, num in enumerate(D):
        for l, r in L:
            if index + r + 1 <= N:
                D[index+l:index+r+1] = [_+num for _ in D[index+l:index+r+1]]
            elif index+l <= N-1:
                D[index+l:N] = [_+num for _ in D[index+l:N]]
    print(D[N-1] % 998244353)
                
    
    
if __name__ == "__main__":
    main()

Fixed submission:
import sys
import math
from collections import defaultdict, deque, Counter
from copy import deepcopy
from bisect import bisect, bisect_right, bisect_left
from heapq import heapify, heappop, heappush
    
input = sys.stdin.readline
def RD(): return input().rstrip()
def F(): return float(input().rstrip())
def I(): return int(input().rstrip())
def MI(): return map(int, input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int, input().split()))
def TI(): return tuple(map(int, input().split()))
def LF(): return list(map(float,input().split()))
def Init(H, W, num): return [[num for i in range(W)] for j in range(H)]
    

def main():
    N, K = MI()
    L = [LI() for i in range(K)]
    D = [0] * N
    D[0] = 1
    D[1] = -1
    num = 0
    mod = 998244353
    for index in range(N):
        num += D[index] % mod
        for l, r in L:
            if index + r + 1 <= N-1:
                D[index+l] += num
                D[index+r+1] -= num
            elif index+l <= N-1:
                D[index+l] += num
                
    print(num % mod)
    
if __name__ == "__main__":
    main()