A: Information Search

problem

The posting list is a list in which there is a correspondence between the search term and the appearing document ID. For example

* Hokkaido: 1, 2, 4, 9
* Sightseeing: 1, 3, 4, 7



And so on.

From the above posting list, if you search for and, the document with ID 1, 4 will be hit, and if you search for or, ID 1, 2, 3, 4, 7, 9 will be hit.

Here, and search means "listing elements contained in either list", or search means "listing elements contained in at least one of the lists".

Since the posting list is given, output the results of and search and or search respectively.

Input format


n m
a_1 a_2 $ \ ldots $ a_n
b_1 b_2 $ \ ldots $ b_m


All inputs consist of integers.

The first line gives the lengths n and m of the two posting lists to search, separated by spaces.

The second and third lines are given the IDs contained in their respective posting lists, separated by blanks.

Constraint

* 1 \ leq n, m \ leq 2 \ times 10 ^ 5
* a_i <a_j (i <j)
* b_i <b_j (i <j)
* 1 \ leq a_i, b_i \ leq 10 ^ 9



Output format

Let A be the number of hits in the and search, and B be the number of hits in the or search.

Print on the first line in the order A B, separated by blanks.

Output the IDs hit by and search on the following line A in ascending order.

Output the IDs hit by or search on the following B line in ascending order.

Input example 1


4 4
1 2 4 9
1 3 4 7


Output example 1


2 6
1
Four
1
2
3
Four
7
9


Input example 2


4 4
1 3 5 7
2 4 6 8


Output example 2


0 8
1
2
3
Four
Five
6
7
8


Input example 3


3 5
one two Three
1 2 3 4 5


Output example 3


3 5
1
2
3
1
2
3
Four
Five






Example

Input

4 4
1 2 4 9
1 3 4 7


Output

2 6
1
4
1
2
3
4
7
9
// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// stream
//#include <istream>
#include <sstream>
//#include <ostream>
#include <fstream>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)std::cin>>w;
// output
#define OUT(dist) std::cout<<(dist);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t:" << (dist) << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define REP(w, n) for(int w=0;w<int(n);++w)
#define RREP(w, n) for(int w=int(n)-1;w>=0;--w)
#define FORLL(w, a, n) for(ll w=ll(a);w<ll(n);++w)
#define RFORLL(w, a, n) for(ll w=ll(n)-1;w>=ll(a);--w)
#define REPLL(w, n) for(ll w=0;w<ll(n);++w)
#define RREPLL(w, n) for(ll w=ll(n)-1;w>=0;--w)
#define IN(a, x, b) (a<=x && x<b)
template<class T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
//void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }
// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;

template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

#define random_shuffle "USE std::shuffle!";

// type/const
#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T& val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T& val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T>& a, const T& val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>>& a, const T& val) { for (auto& b : a) FILL(b, val); }
// ------------>8------------------------------------->8------------



signed main() {
	INIT;

	VAR(int, n, m);
	VEC(int, a, n);
	VEC(int, b, m);

	std::set<int> A, O;
	std::vector<int> ansA, ansO;
	REP(i, n) { A.insert(a[i]); O.insert(a[i]); }
	REP(i, m) {
		if (A.count(b[i])) ansA.emplace_back(b[i]);
		O.insert(b[i]);
	}
	for (auto& x : O) ansO.emplace_back(x);

	OUT(ansA.size())SP OUT(ansO.size())BR;

	std::sort(ALL(ansA));
	std::sort(ALL(ansO));

	for (auto& x : ansA) { OUT(x)BR; }
	for (auto& x : ansO) { OUT(x)BR; }

	return 0;
}
