Problem:
Score : 500 points

Problem Statement

You are given two integers A and B.

Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:

Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.

The set of the squares painted white is divided into exactly A connected components.

The set of the squares painted black is divided into exactly B connected components.

It can be proved that there always exist one or more solutions under the conditions specified in Constraints section.
If there are multiple solutions, any of them may be printed.

Notes

Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.

A set of squares painted white, S, forms a connected component when the following conditions are met:

Any two squares in S are connected.

No pair of a square painted white that is not included in S and a square included in S is connected.

A connected component of squares painted black is defined similarly.

Constraints

1 \leq A \leq 500

1 \leq B \leq 500

Input

Input is given from Standard Input in the following format:

A B

Output

Output should be in the following format:

In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.

Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:

If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be ..

If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be #.

Sample Input 1

2 3

Sample Output 1

3 3
##.
..#
#.#

This output corresponds to the grid below:

Sample Input 2

7 8

Sample Output 2

3 5
#.#.#
.#.#.
#.#.#

Sample Input 3

1 1

Sample Output 3

4 2
..
#.
##
##

Sample Input 4

3 14

Sample Output 4

8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
#.........#..####.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <fstream>
#include <cmath>  
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <numeric>
#include <functional>
#include <string> 
#include <vector>
#include <bitset>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <deque>

using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;

#define REP(i,n) for(int i = 0; i < int(n); i++)
#define REREP(i,n) for(int i = int(n - 1); i >= 0; i--)
#define FOR(i, m, n) for(int i = int(m);i < int(n);i++)
#define REFOR(i, m, n) for(int i = int(n - 1);i >= int(m);i--)
#define ALL(obj) (obj).begin(),(obj).end()

#define VI vector<int>
#define VVI vector<vector<int>>
#define VVVI vector<vector<vector<int>>>
#define VD vector<double>
#define VVD vector<vector<double>>
#define VVVD vector<vector<vector<double>>>
#define VL vector<ll>
#define VVL vector<vector<ll>>
#define VVVL vector<vector<vector<ll>>>
#define VB vector<bool>
#define VVB vector<vector<bool>>
#define VVVB vector<vector<vector<bool>>>
#define VS vector<string>
#define VVS vector<vector<string>>
#define VVVS vector<vector<vector<string>>>

#define PII pair<int,int>
#define PDD pair<double,double>
#define PLL pair<ll,ll>
#define VPII vector<pair<int,int>>
#define VVPII vector<vector<pair<int,int>>>
#define VVVPII vector<vector<vector<pair<int,int>>>>
#define VPLL vector<pair<ll,ll>>
#define VVPLL vector<vector<pair<ll,ll>>>
#define VVVPLL vector<vector<vector<pair<ll,ll>>>>

#define SUMI(obj) accumulate((obj).begin(), (obj).end(), 0)
#define SUMD(obj) accumulate((obj).begin(), (obj).end(), 0.)
#define SUML(obj) accumulate((obj).begin(), (obj).end(), 0LL)
#define SORT(obj) sort((obj).begin(), (obj).end()) // 1,2,3,4,5...
#define RESORT(obj) sort((obj).begin(), (obj).end(), greater<int>()) // 5,4,3,2,1...
#define UB(obj,n) upper_bound((obj).begin(), (obj).end(), n) //itr > n
#define LB(obj,n) lower_bound((obj).begin(), (obj).end(), n) //itr>= n

const ll MOD = (ll)1e9 + 7;
const ll HINF = (ll)1e18;
const ll LINF = (ll)1e9;

//integer
class Integer {
public:
	int gcd(int a, int b) {
		if (a == 0 || b == 0) return 0;
		if (a < b) swap(a, b);
		while (b != 0) {
			a = a%b;
			swap(a, b);
		}
		return a;
	}

	int lcm(int a, int b) {
		if (a == 0 || b == 0) return 0;
		return a / gcd(a, b)*b;
	}
};

//eratosthenes
class Eratosthenes{
public:
	vector<bool> primary(int N) {
		vector<bool> primary(N + 1, true);
		primary[0] = false;
		if (N == 0) return primary;
		primary[1] = false;
		for (int i = 1; i*i <= N; i++) if (primary[i]) for (int j = 2 * i; j <= N; j += i) primary[j] = false;
		return primary;
	}
};

//combination mod
class Combination_Mod {
public:
	VL factorial;

	//N! table
	void set(ll N, ll quotient){
		factorial.resize(N + 1, 1);
		for (ll i = 1; i <= N; i++) {
			factorial[i] *= factorial[i - 1] * i;
			factorial[i] %= quotient;
		}
		return;
	}

	//repeat square method y = x^n mod quotient 
	ll rsm(ll x, ll n, ll quotient) {
		ll y = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				y *= x;
				y %= quotient;
			}
			x *= x;
			x %= quotient;
			n >>= 1;
		}
		return y;
	}

	//modulus of nCk - combination mod 
	ll nCk(ll n, ll k, ll quotient) {
		if (n < k || k == 0) return 0;
		ll nCk = (factorial[n] % quotient);
		nCk *= rsm(factorial[k], quotient - 2, quotient);
		nCk %= quotient;
		nCk *= rsm(factorial[n - k], quotient - 2, quotient);
		return (nCk % quotient);
	}
};

//union-find
class Union_Find {
public:
	VI node;
	void set(int n){
		node.resize(n);
		REP(i, n) node[i] = i;
	}

	int root(int n) {
		if (node[n] == n) return n;
		else return node[n] = root(node[n]);
	}

	void unite(int n, int m) {
		if (n > m) swap(n, m);
		n = root(n);
		m = root(m);
		if (n == m) return;
		else node[m] = n;
	}
};

//dijkstra
class Dijkstra{
public:
	VVPII edge;
	VVI dist;
	void set(int N, int inf){
		edge.resize(N);
		dist.resize(N);
		REP(i, N) dist[i].resize(N);
		REP(i, N)REP(j, N) dist[i][j] = inf;
	}

	void make_edge(int from, int to, int cost) {
		edge[from].push_back({ to,cost });
	}

	void dijkstra(int start) {
		priority_queue<PII, vector<PII>, greater<PII>> pq;
		dist[start][start] = 0;
		pq.push({ 0,start });
		while (!pq.empty()) {
			int from = pq.top().second;
			pq.pop();
			REP(i, edge[from].size()) {
				int to = edge[from][i].first;
				if (dist[start][to] > dist[start][from] + edge[from][i].second) {
					dist[start][to] = dist[start][from] + edge[from][i].second;
					pq.push({ dist[start][from] + edge[from][i].second,to });
				}
			}
		}
	}
};

//bellman-ford
class Bellman_Ford {
public:
	struct edge{
		int from, to, cost;
	};
	int N;
	VI node;
	vector<edge> graph;

	void set(int node_, int inf) {
		N = node_;
		node.resize(node_);
	}

	void make_edge(int from,int to, int cost){
		graph.push_back({from,to,cost});
	}

	void bellman_ford(int start,int inf) {
		REP(i, N) node[i] = inf;
		node[start] = 0;		
		REP(i, N - 1) REP(j, graph.size()) if (node[graph[j].to] > node[graph[j].from] + graph[j].cost) node[graph[j].to] = node[graph[j].from] + graph[j].cost;
	}
};

//ford fulkerson
class Ford_Fulkerson{
public:
	struct edge {
		int to, cap, rev;
	};

	int node, start, goal;
	vector<vector<edge>> graph;
	vector<bool> visit;

	void set(int node_, int start_, int goal_) {
		node = node_;
		start = start_;
		goal = goal_;
		graph.resize(node);
		visit.resize(node);
	}

	void make_edge(int from, int to, int cap) {
		graph[from].push_back({ to,cap,(int)graph[to].size() });
		graph[to].push_back({ from,0,(int)graph[from].size() - 1 });
	}

	int dfs(int from, int flow) {
		if (from == goal) return flow;
		visit[from] = false;
		REP(i, graph[from].size()) {
			if (visit[graph[from][i].to] && (graph[from][i].cap > 0)) {
				int dflow = dfs(graph[from][i].to, min(flow, graph[from][i].cap));
				if (dflow > 0) {
					graph[from][i].cap -= dflow;
					graph[graph[from][i].to][graph[from][i].rev].cap += dflow;
					return dflow;
				}
			}
		}
		return 0;
	}

	int maxflow(void) {
		int maxflow = 0;
		while (1) {
			REP(i, graph.size()) visit[i] = true;
			int flow = dfs(start, 1);
			if (flow == 0) return maxflow;
			maxflow += flow;
		}
	}
};

//least common ancestor
class Least_Common_Ancestor {
public:
	int node;
	int MAXLOG2;
	VVI edge;
	VI depth;
	VVI parent;

	void set(int node_, int MAXLOG2_) {
		node = node_;
		MAXLOG2 = MAXLOG2_;
		edge.resize(node);
		depth.resize(node);
		parent.resize(node);
		REP(i, node) parent[i].resize(MAXLOG2);
	}

	void dfs(int root, int root_from) {
		depth[root] = 0;
		parent[root][0] = root_from;
		stack<pair<int, int>> st;
		st.push({ root,root_from });

		while (!st.empty()) {
			int from = st.top().first;
			int from_from = st.top().second;
			st.pop();
			REP(i, edge[from].size()) {
				int to = edge[from][i];
				if (to != from_from) {
					depth[to] = depth[from] + 1;
					parent[to][0] = from;
					st.push({ to,from });
				}
			}
		}
		return;
	}

	//make table
	void initialize(int N) {
		REP(k, MAXLOG2 - 1) {
			REP(i, N) {
				if (parent[i][k] < 0) parent[i][k + 1] = -1;
				else parent[i][k + 1] = parent[parent[i][k]][k];
			}
		}
		return;
	}

	//get least common ancestor
	int get(int a, int b) {
		if (depth[a] > depth[b]) swap(a, b);
		REP(k, MAXLOG2 - 1) if (((depth[b] - depth[a]) >> k) & 1) b = parent[b][k];
		if (a == b) return a;
		REREP(k, MAXLOG2) {
			if (parent[a][k] != parent[b][k]) {
				a = parent[a][k];
				b = parent[b][k];
			}
		}
		return parent[a][0];
	}
};

//directed acyclic graph
class Directed_Acyclic_Graph{
public:

	int N;
	Dijkstra dijkstra;
	struct edge {
		int dest, cost;
		bool need;
	};
	vector<vector<edge>> output;
	VI input;
	VI topological_order;

	void set(int N_, int inf){
		N = N_;
		dijkstra.set(N, inf);
		output.resize(N);
		input.resize(N,0);
	}

	void make_edge(int from, int to, int cost){
		dijkstra.make_edge(from, to, cost);
		output[from].push_back({to, cost, true});
	}

	void make_dag(int start) {
		dijkstra.dijkstra(start);
		REP(i, N) {
			REP(j, output[i].size()) {
				int from = i;
				edge &e = output[i][j];
				if (dijkstra.dist[start][e.dest] - dijkstra.dist[start][from] != e.cost) e.need = false;
			}
		}
	}

	bool topological_sort(int start){
		REP(i, N) REP(j, output[i].size()) if (output[i][j].need) input[output[i][j].dest]++;

		stack<int> st;
		st.push(start);
		while(!st.empty()){
			int from = st.top();
			st.pop();
			topological_order.push_back(from);
			REP(i, output[from].size()) {
				edge &e = output[from][i];
				if (e.need) {
					input[e.dest]--;
					if (input[e.dest] == 0) st.push(e.dest);
				}
			}
		}
		
		bool valid = true;
		REP(i, N) if (input[i] > 0) valid = false;
		return valid;
	}	
};


void YN(bool flag){
	cout << ((flag) ? "YES" : "NO") << endl;
}

void Yn(bool flag) {
	cout << ((flag) ? "Yes" : "No") << endl;
}

void yn(bool flag) {
	cout << ((flag) ? "yes" : "no") << endl;
}


int main() {
	int A, B; cin >> A >> B;
	int h = 100, w = 100;
	VS S(h);

	REP(i,h/2) REP(j, w) S[i] += '.';
	FOR(i,h/2 ,h) REP(j, w) S[i] += '#';


	REP(i,(B - 1)/(w/2) + 1){
		if(i != (B - 1) / (h / 2)){
			REP(j,w){
				if (j % 2 == 0) S[2 * i][j] = '#';
			}
		}
		else{
			REP(j,(B - 1)%(w/2)){
				S[2 * i][2*j] = '#';
			}
		}
	}

	REP(i, (A - 1) / (w / 2) + 1) {
		if (i != (A - 1) / (h / 2)) {
			REP(j, w) {
				if (j % 2 == 0) S[2 * i + h/2 + 1][j] = '.';
			}
		}
		else {
			REP(j, (A - 1) % (w / 2)) {
				S[2 * i + h / 2 + 1][2 * j] = '.';
			}
		}
	}


	REP(i, h) cout << S[i] << endl;



	return 0;
}