#include <bits/stdc++.h>

// O(NK) 解法
[[nodiscard]] static inline constexpr uint_fast64_t solve(const uint_fast32_t N, const uint_fast32_t K, const std::vector<uint_least32_t>& A, const std::vector<uint_least32_t>& B) noexcept
{
	std::array<std::vector<std::array<uint_least64_t, 2>>, 2> dp = { std::vector<std::array<uint_least64_t, 2>>(K + 1, { 0, 0 }), std::vector<std::array<uint_least64_t, 2>>(K + 1, { 0, 0 }) };
	dp[1][0] = { A[0], 0 };
	for (uint_fast32_t j = 1; j <= K; ++j)
		dp[1][j] = { A[0], B[0] };

	for (uint_fast32_t i = 1; i < N; ++i)
	{
		dp[(i & 1) ^ 1][0] = { dp[i & 1][0][0] + A[i], 0 };
		for (uint_fast32_t j = 1; j <= K; ++j)
			dp[(i & 1) ^ 1][j] = { std::max<uint_fast64_t>(dp[i & 1][j][0], dp[i & 1][j - 1][1]) + A[i], std::max<uint_fast64_t>(dp[i & 1][j - 1][0], dp[i & 1][j][1]) + B[i] };
	}

	return std::max<uint_fast64_t>(dp[N & 1][K][0], dp[N & 1][K][1]);
}

int main()
{
	std::cin.tie(nullptr);
	std::ios::sync_with_stdio(false);

	uint_fast32_t N, K;
	std::cin >> N >> K;
	std::vector<uint_least32_t> A(N), B(N);
	for (auto& a : A) std::cin >> a;
	for (auto& b : B) std::cin >> b;

	std::cout << solve(N, K, A, B) << '\n';
	return 0;
}