Problem: Another feature of Shakespeare language is that the variables are named after characters of plays by Shakespeare, and all operations on them (value assignment, output etc.) look like a dialog with other characters. New values of variables are defined in a rather lengthy way, so a programmer should try to minimize their usage.

You have to print the given sequence of n integers. To do this, you have m variables and two types of operations on them:

  * variable=integer
  * print(variable)



Any of the m variables can be used as variable. Variables are denoted by lowercase letters between "a" and "z", inclusive. Any integer number can be used as integer.

Let's say that the penalty for using first type of operations equals to the number of set bits in the number integer. There is no penalty on using second type of operations. Find and output the program which minimizes the penalty for printing the given sequence of numbers.

Input

The first line of input contains integers n and m (1 ≤ n ≤ 250, 1 ≤ m ≤ 26). The second line contains the sequence to be printed. Each element of the sequence is an integer between 1 and 109, inclusive. The sequence has to be printed in the given order (from left to right).

Output

Output the number of lines in the optimal program and the optimal penalty. Next, output the program itself, one command per line. If there are several programs with minimal penalty, output any of them (you have only to minimize the penalty).

Examples

Input

7 2
1 2 2 4 2 1 2


Output

11 4
b=1
print(b)
a=2
print(a)
print(a)
b=4
print(b)
print(a)
b=1
print(b)
print(a)


Input

6 3
1 2 3 1 2 3


Output

9 4
c=1
print(c)
b=2
print(b)
a=3
print(a)
print(c)
print(b)
print(a)

Solution (in JAVA):

Solution:
/**
 * Created by IntelliJ IDEA.
 * User: mac
 * Date: 11-12-3
 * Time: 下午9:56
 * To change this template use File | Settings | File Templates.
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class E {

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(reader.readLine());
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    Vertex vs, vt, S, T;
    Vertex[] in, out;

    int n, m;
    int[] a;

    void dfs(Vertex at, char cur, int last, List<String>[] before, char[] which) {
        int id = at.id;
        if (at == T)
            return;

        if (at == in[id]) {
            which[id] = cur;
            if (last == -1 || a[id] != a[last]) {
                before[id].add(cur + "=" + a[id]);
            }
            dfs(out[id], cur, last, before, which);
        } else {
            for (Edge e : at) {
                if (e.t.id > id && e.cap == 0) {
                    dfs(e.t, cur, id, before, which);
                    return;
                }
            }
        }
    }

    void print(List<String>[] before, char[] which) {
        char cur = 'a';
        for (Edge e : S) {
            if (e.t.id != -1 && e.cap == 0) {
                dfs(e.t, cur, -1, before, which);
                ++cur;
            }
        }
    }

    void solve() throws IOException {
        n = nextInt();
        m = nextInt();
        a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
        }

        vs = new Vertex();
        vt = new Vertex();
        S = new Vertex();
        T = new Vertex();
        in = new Vertex[n];
        out = new Vertex[n];

        for (int i = 0; i < n; i++) {
            in[i] = new Vertex(i);
            out[i] = new Vertex(i);
        }
        vs.addEdge(S, m, 0);
        T.addEdge(vt, m, 0);
        S.addEdge(T, m, 0);

        final int BIG = 100000;

        for (int i = 0; i < n; i++) {
            S.addEdge(in[i], 1, Integer.bitCount(a[i]));

            in[i].addEdge(out[i], 1, -BIG);

            for (int j = i + 1; j < n; j++) {
                if (a[i] == a[j])
                    out[i].addEdge(in[j], 1, 0);
                else
                    out[i].addEdge(in[j], 1, Integer.bitCount(a[j]));
            }

            out[i].addEdge(T, 1, 0);
        }

        Vertex[] all = Vertex.vertexList.toArray(new Vertex[0]);

        Result result = MinCostFlowUtils.minCostFlow(all, vs, vt);

        @SuppressWarnings({"unchecked"})
        List<String>[] before = new List[n];
        for (int i = 0; i < before.length; i++) {
            before[i] = new ArrayList<String>();
        }
        char[] which = new char[n];
        print(before, which);
        int nLines = n;
        for (List<String> strings : before) {
            nLines += strings.size();
        }

        int ans = result.cost + BIG * n;
        writer.println(nLines + " " + ans);
        for (int i = 0; i < n; i++) {
            for (String s : before[i]) {
                writer.println(s);
            }
            writer.println("print(" + which[i] + ")");
        }
    }

    static public void main(String[] args) {
        new E().run();
    }
}

class Edge {
    Vertex t;
    int cap, cost;
    Edge rev;

    Edge(Vertex t, int cap, int cost) {
        this.t = t;
        this.cap = cap;
        this.cost = cost;
    }
}

class Vertex extends ArrayList<Edge> {
    boolean inQueue = false;
    int dist;
    int am;
    Edge prev;
    int id;//in a

    void addEdge(Vertex t, int cap, int cost) {
        Edge ab = new Edge(t, cap, cost);
        Edge ba = new Edge(this, 0, -cost);
        ab.rev = ba;
        ba.rev = ab;
        add(ab);
        t.add(ba);
    }

    static List<Vertex> vertexList = new ArrayList<Vertex>();

    Vertex() {
        this.id = -1;
        vertexList.add(this);
    }

    Vertex(int id) {
        this.id = id;
        vertexList.add(this);
    }
}

class Result {
    int cost, flow;

    Result(int cost, int flow) {
        this.cost = cost;
        this.flow = flow;
    }
}

class MinCostFlowUtils {

    static Result minCostFlow(Vertex[] vs, Vertex s, Vertex t) {
        int flow = 0, cost = 0;

        for (; ; ) {
            for (Vertex v : vs) {
                v.inQueue = false;
                v.dist = Integer.MAX_VALUE;
            }
            LinkedList<Vertex> queue = new LinkedList<Vertex>();
            s.dist = 0;
            s.inQueue = true;
            s.am = Integer.MAX_VALUE;
            queue.add(s);
            while (!queue.isEmpty()) {
                Vertex u = queue.poll();
                u.inQueue = false;
                for (Edge e : u)
                    if (e.cap > 0) {
                        Vertex v = e.t;
                        int nc = u.dist + e.cost;
                        if (nc < v.dist) {
                            v.dist = nc;
                            v.prev = e;
                            v.am = Math.min(u.am, e.cap);
                            if (!v.inQueue) {
                                v.inQueue = true;
                                if (queue.isEmpty() || v.dist < queue.peek().dist)
                                    queue.addFirst(v);
                                else
                                    queue.addLast(v);
                            }
                        }
                    }
            }

            if (t.dist == Integer.MAX_VALUE)
                break;

            int by = t.am;
            flow += by;
            cost += by * t.dist;

            Vertex u = t;
            while (u != s) {
                Edge e = u.prev;
                e.cap -= by;
                e.rev.cap += by;
                u = e.rev.t;
            }
        }

        return new Result(cost, flow);
    }
}