Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353

class BIT:
    def __init__(self, n, init=None):
        self.size = n
        if init is None:
            self.v = [0] * (n + 1) # don't use bit[0]
        else:
            self.v = [0] + init
            for i in range(1, n):
                if i + (i & -i) <= n: self.v[i + (i & -i)] += self.v[i]

    def sum(self, i):
        '''
        Calculate a[1] + ... + a[i]
        '''
        S = 0
        while i > 0:
            S += self.v[i]
            i -= i & -i
        return S
    
    def modsum(self, i, mod):
        '''
        Calculate a[1] + ... + a[i]
        '''
        S = 0
        while i > 0:
            S += self.v[i]
            S %= mod
            i -= i & -i
        return S


    def add(self, i, x):
        '''
        set a[i] to be a[i] + x
        '''
        assert i > 0
        while i <= self.size:
            self.v[i] += x
            i += i & -i

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
bit = BIT(N + 1)
bit.v[1] = 1
for i in range(1, N + 1):
    temp = bit.sum(i)
    for s, t in segments:
        if i + s <= N:
            bit.add(i + s, temp)
            bit.add(min(i + t + 1, N + 1), -temp)
print(bit.modsum(N, MOD))

Fixed submission:
MOD = 998244353

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
dp = [0] * (2 * N + 1)
for i in range(N):
    for s, t in segments:
        t += 1
        dp[i + s] += dp[i] if i != 0 else 1
        dp[i + t] -= dp[i] if i != 0 else 1
    dp[i + 1] += dp[i]
    dp[i + 1] %= MOD
print(dp[N - 1])

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353

class BIT:
    def __init__(self, n, init=None):
        self.size = n
        if init is None:
            self.v = [0] * (n + 1) # don't use bit[0]
        else:
            self.v = [0] + init
            for i in range(1, n):
                if i + (i & -i) <= n: self.v[i + (i & -i)] += self.v[i]

    def sum(self, i):
        '''
        Calculate a[1] + ... + a[i]
        '''
        S = 0
        while i > 0:
            S += self.v[i]
            i -= i & -i
        return S
    
    def modsum(self, i, mod):
        '''
        Calculate a[1] + ... + a[i]
        '''
        S = 0
        while i > 0:
            S += self.v[i]
            S %= mod
            i -= i & -i
        return S


    def add(self, i, x):
        '''
        set a[i] to be a[i] + x
        '''
        assert i > 0
        while i <= self.size:
            self.v[i] += x
            i += i & -i

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
bit = BIT(N + 1)
bit.v[1] = 1
for i in range(1, N + 1):
    temp = bit.sum(i)
    for s, t in segments:
        if i + s <= N:
            bit.add(i + s, temp)
            bit.add(min(i + t + 1, N + 1), -temp)
print(bit.modsum(N, MOD))

Fixed submission:
MOD = 998244353

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
dp = [0] * (2 * N + 1)
for i in range(N):
    for s, t in segments:
        t += 1
        dp[i + s] += dp[i] if i != 0 else 1
        dp[i + t] -= dp[i] if i != 0 else 1
    dp[i + 1] += dp[i]
    dp[i + 1] %= MOD
print(dp[N - 1])

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 998244353

class BIT:
    def __init__(self, n, init=None):
        self.size = n
        if init is None:
            self.v = [0] * (n + 1) # don't use bit[0]
        else:
            self.v = [0] + init
            for i in range(1, n):
                if i + (i & -i) <= n: self.v[i + (i & -i)] += self.v[i]

    def sum(self, i):
        '''
        Calculate a[1] + ... + a[i]
        '''
        S = 0
        while i > 0:
            S += self.v[i]
            i -= i & -i
        return S

    def add(self, i, x):
        '''
        set a[i] to be a[i] + x
        '''
        assert i > 0
        while i <= self.size:
            self.v[i] += x
            i += i & -i

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
bit = BIT(N + 1)
bit.v[1] = 1
for i in range(1, N + 1):
    temp = bit.sum(i)
    for s, t in segments:
        if i + s <= N:
            bit.add(i + s, temp)
            bit.add(min(i + t + 1, N + 1), -temp)
print(bit.sum(N) % MOD)

Fixed submission:
MOD = 998244353

N, K = map(int, input().split())
segments = [tuple(map(int, input().split())) for _ in range(K)]
dp = [0] * (2 * N + 1)
for i in range(N):
    for s, t in segments:
        t += 1
        dp[i + s] += dp[i] if i != 0 else 1
        dp[i + t] -= dp[i] if i != 0 else 1
    dp[i + 1] += dp[i]
    dp[i + 1] %= MOD
print(dp[N - 1])