Buggy python submission (verdict: Time Limit Exceeded):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from sys import exit

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

#####segfunc#####
def segfunc(x, y):
    return min(x, y)
#################

#####ide_ele#####
ide_ele = 2 ** 63 - 1
#################

class LazySegmentTree:
    """
    init(init_val, ide_ele): 配列init_valで初期化 O(N)
    add(l, r, x): 区間[l, r)にxを加算 O(logN)
    query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
    """
    def __init__(self, init_val, segfunc, ide_ele):
        """
        init_val: 配列の初期値
        segfunc: 区間にしたい操作
        ide_ele: 単位元
        num: n以上の最小の2のべき乗
        data: 値配列(1-index)
        lazy: 遅延配列(1-index)
        """
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.data = [ide_ele] * 2 * self.num
        self.lazy = [0] * 2 * self.num
        # 配列の値を葉にセット
        for i in range(n):
            self.data[self.num + i] = init_val[i]
        # 構築していく
        for i in range(self.num - 1, 0, -1):
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1])

    def gindex(self, l, r):
            """
            伝搬する対象の区間を求める
            lm: 伝搬する必要のある最大の左閉区間
            rm: 伝搬する必要のある最大の右開区間
            """
            l += self.num
            r += self.num
            lm = l >> (l & -l).bit_length()
            rm = r >> (r & -r).bit_length()

            while r > l:
                if l <= lm:
                    yield l
                if r <= rm:
                    yield r
                r >>= 1
                l >>= 1
            while l:
                yield l
                l >>= 1

    def propagates(self, *ids):
        """
        遅延伝搬処理
        ids: 伝搬する対象の区間
        """
        for i in reversed(ids):
            v = self.lazy[i]
            if not v:
                continue
            self.lazy[2 * i] += v
            self.lazy[2 * i + 1] += v
            self.data[2 * i] += v
            self.data[2 * i + 1] += v
            self.lazy[i] = 0

    def add(self, l, r, x):
        """
        区間[l, r)の値にxを加算
        l, r: index(0-index)
        x: additional value
        """
        *ids, = self.gindex(l, r)
        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                self.lazy[l] += x
                self.data[l] += x
                l += 1
            if r & 1:
                self.lazy[r - 1] += x
                self.data[r - 1] += x
            r >>= 1
            l >>= 1
        for i in ids:
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1]) + self.lazy[i]


    def query(self, l, r):
        """
        [l, r)のsegfuncしたものを得る
        l: index(0-index)
        r: index(0-index)
        """
        *ids, = self.gindex(l, r)
        self.propagates(*ids)

        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.data[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.data[r - 1])
            l >>= 1
            r >>= 1
        return res

# 1 ~ Nまで
N, K = getNM()
que = [getList() for i in range(K)]

# 通りの数を求める問題
# dp？
# 組み合わせ？

# goの要素を足して行ってN = 1を達成できればいい
# ただしgoの数が多い
# ナップサックは無理

# 重複あり部分和
# 部分和の通り

# どうすればN - 1の組み合わせができるか
# ソートする？
# 足し合わせ？


dp = [0] * (N + 1)
seg = LazySegmentTree([0] * (N + 1), segfunc, ide_ele)
dp[1] = 1
seg.add(1, 2, 1)

# dpする
for i in range(1, N):
    dp[i] = seg.query(i, i + 1) % mod
    for l, r in que:
        if i + l <= N:
            seg.add(i + l, min(i + r + 1, N + 1), dp[i])
        else:
            continue
print(seg.query(N, N + 1) % mod)

Fixed submission:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from sys import exit

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

N, K = getNM()
que = [getList() for i in range(K)]

dp = [0] * (N + 1)
dp[1] = 1
dp[2] = -1

for i in range(1, N + 1):
    dp[i] += dp[i - 1]
    dp[i] %= mod
    for l, r in que:
        if i + l <= N:
            dp[i + l] += dp[i]
        if i + r + 1 <= N:
            dp[i + r + 1] -= dp[i]
print(dp[N] % mod)

Buggy python submission (verdict: Time Limit Exceeded):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from sys import exit

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

#####segfunc#####
def segfunc(x, y):
    return min(x, y)
#################

#####ide_ele#####
ide_ele = 2 ** 63 - 1
#################

class LazySegmentTree:
    """
    init(init_val, ide_ele): 配列init_valで初期化 O(N)
    add(l, r, x): 区間[l, r)にxを加算 O(logN)
    query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
    """
    def __init__(self, init_val, segfunc, ide_ele):
        """
        init_val: 配列の初期値
        segfunc: 区間にしたい操作
        ide_ele: 単位元
        num: n以上の最小の2のべき乗
        data: 値配列(1-index)
        lazy: 遅延配列(1-index)
        """
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.data = [ide_ele] * 2 * self.num
        self.lazy = [0] * 2 * self.num
        # 配列の値を葉にセット
        for i in range(n):
            self.data[self.num + i] = init_val[i]
        # 構築していく
        for i in range(self.num - 1, 0, -1):
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1])

    def gindex(self, l, r):
            """
            伝搬する対象の区間を求める
            lm: 伝搬する必要のある最大の左閉区間
            rm: 伝搬する必要のある最大の右開区間
            """
            l += self.num
            r += self.num
            lm = l >> (l & -l).bit_length()
            rm = r >> (r & -r).bit_length()

            while r > l:
                if l <= lm:
                    yield l
                if r <= rm:
                    yield r
                r >>= 1
                l >>= 1
            while l:
                yield l
                l >>= 1

    def propagates(self, *ids):
        """
        遅延伝搬処理
        ids: 伝搬する対象の区間
        """
        for i in reversed(ids):
            v = self.lazy[i]
            if not v:
                continue
            self.lazy[2 * i] += v
            self.lazy[2 * i + 1] += v
            self.data[2 * i] += v
            self.data[2 * i + 1] += v
            self.lazy[i] = 0

    def add(self, l, r, x):
        """
        区間[l, r)の値にxを加算
        l, r: index(0-index)
        x: additional value
        """
        *ids, = self.gindex(l, r)
        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                self.lazy[l] += x
                self.data[l] += x
                l += 1
            if r & 1:
                self.lazy[r - 1] += x
                self.data[r - 1] += x
            r >>= 1
            l >>= 1
        for i in ids:
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1]) + self.lazy[i]


    def query(self, l, r):
        """
        [l, r)のsegfuncしたものを得る
        l: index(0-index)
        r: index(0-index)
        """
        *ids, = self.gindex(l, r)
        self.propagates(*ids)

        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.data[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.data[r - 1])
            l >>= 1
            r >>= 1
        return res

# 1 ~ Nまで
N, K = getNM()
que = [getList() for i in range(K)]

# 通りの数を求める問題
# dp？
# 組み合わせ？

# goの要素を足して行ってN = 1を達成できればいい
# ただしgoの数が多い
# ナップサックは無理

# 重複あり部分和
# 部分和の通り

# どうすればN - 1の組み合わせができるか
# ソートする？
# 足し合わせ？


dp = [0] * (N + 1)
seg = LazySegmentTree([0] * (N + 1), segfunc, ide_ele)
dp[1] = 1
seg.add(1, 2, 1)

# dpする
for i in range(1, N):
    dp[i] = seg.query(i, i + 1) % mod
    for l, r in que:
        if i + l <= N:
            seg.add(i + l, min(i + r + 1, N + 1), dp[i])
print(seg.query(N, N + 1) % mod)

Fixed submission:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from sys import exit

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

N, K = getNM()
que = [getList() for i in range(K)]

dp = [0] * (N + 1)
dp[1] = 1
dp[2] = -1

for i in range(1, N + 1):
    dp[i] += dp[i - 1]
    dp[i] %= mod
    for l, r in que:
        if i + l <= N:
            dp[i + l] += dp[i]
        if i + r + 1 <= N:
            dp[i + r + 1] -= dp[i]
print(dp[N] % mod)

Buggy python submission (verdict: Time Limit Exceeded):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
from heapq import heapify, heappop, heappush
import math
import random
import string
from copy import deepcopy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

#####segfunc#####
def segfunc(x, y):
    return min(x, y)
#################

#####ide_ele#####
ide_ele = 2 ** 63 - 1
#################

class LazySegmentTree:
    """
    init(init_val, ide_ele): 配列init_valで初期化 O(N)
    add(l, r, x): 区間[l, r)にxを加算 O(logN)
    query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
    """
    def __init__(self, init_val, segfunc, ide_ele):
        """
        init_val: 配列の初期値
        segfunc: 区間にしたい操作
        ide_ele: 単位元
        num: n以上の最小の2のべき乗
        data: 値配列(1-index)
        lazy: 遅延配列(1-index)
        """
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.data = [ide_ele] * 2 * self.num
        self.lazy = [0] * 2 * self.num
        # 配列の値を葉にセット
        for i in range(n):
            self.data[self.num + i] = init_val[i]
        # 構築していく
        for i in range(self.num - 1, 0, -1):
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1])

    def gindex(self, l, r):
            """
            伝搬する対象の区間を求める
            lm: 伝搬する必要のある最大の左閉区間
            rm: 伝搬する必要のある最大の右開区間
            """
            l += self.num
            r += self.num
            lm = l >> (l & -l).bit_length()
            rm = r >> (r & -r).bit_length()

            while r > l:
                if l <= lm:
                    yield l
                if r <= rm:
                    yield r
                r >>= 1
                l >>= 1
            while l:
                yield l
                l >>= 1

    def propagates(self, *ids):
        """
        遅延伝搬処理
        ids: 伝搬する対象の区間
        """
        for i in reversed(ids):
            v = self.lazy[i]
            if not v:
                continue
            self.lazy[2 * i] += v
            self.lazy[2 * i + 1] += v
            self.data[2 * i] += v
            self.data[2 * i + 1] += v
            self.lazy[i] = 0

    def add(self, l, r, x):
        """
        区間[l, r)の値にxを加算
        l, r: index(0-index)
        x: additional value
        """
        *ids, = self.gindex(l, r)
        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                self.lazy[l] += x
                self.data[l] += x
                l += 1
            if r & 1:
                self.lazy[r - 1] += x
                self.data[r - 1] += x
            r >>= 1
            l >>= 1
        for i in ids:
            self.data[i] = self.segfunc(self.data[2 * i], self.data[2 * i + 1]) + self.lazy[i]


    def query(self, l, r):
        """
        [l, r)のsegfuncしたものを得る
        l: index(0-index)
        r: index(0-index)
        """
        *ids, = self.gindex(l, r)
        self.propagates(*ids)

        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.data[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.data[r - 1])
            l >>= 1
            r >>= 1
        return res

# 1 ~ Nまで
N, K = getNM()
que = [getList() for i in range(K)]

# 通りの数を求める問題
# dp？
# 組み合わせ？

"""
go = set()
for l, r in que:
    for i in range(l, r + 1):
        go.add(i)
"""

# goの要素を足して行ってN = 1を達成できればいい
# ただしgoの数が多い
# ナップサックは無理

# 重複あり部分和
# 部分和の通り

# どうすればN - 1の組み合わせができるか
# ソートする？
# 足し合わせ？

"""
ナイーブな解法
go = list(go)

dp = [0] * (N + 1)
dp[1] = 1

for i in range(1, N + 1):
    for j in range(len(go)):
        if i + go[j] <= N:
            dp[i + go[j]] += dp[i]
    dp[i] %= mod
print(dp[N] % mod)
"""

dp = [0] * (N + 1)
seg = LazySegmentTree([0] * (N + 1), segfunc, ide_ele)
dp[1] = 1
seg.add(1, 2, 1)


# dpする
for i in range(1, N):
    dp[i] = seg.query(i, i + 1) % mod
    for l, r in que:
        if i + l <= N:
            seg.add(i + l, min(i + r + 1, N + 1), dp[i])
print(seg.query(N, N + 1) % mod)

Fixed submission:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from sys import exit

import sys
sys.setrecursionlimit(1000000000)
mod = 998244353

#############
# Main Code #
#############

N, K = getNM()
que = [getList() for i in range(K)]

dp = [0] * (N + 1)
dp[1] = 1
dp[2] = -1

for i in range(1, N + 1):
    dp[i] += dp[i - 1]
    dp[i] %= mod
    for l, r in que:
        if i + l <= N:
            dp[i + l] += dp[i]
        if i + r + 1 <= N:
            dp[i + r + 1] -= dp[i]
print(dp[N] % mod)