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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = 1000000000;
vector<int> hung(const vector<vector<int> > &A) {
  int n = A.size();
  int m = A[0].size();
  vector<vector<long long> > a(n + 1);
  a[0] = vector<long long>(m + 1);
  for (int i = 0; i < n; ++i) {
    a[i + 1].push_back(100LL * INF);
    for (int j = 0; j < m; ++j) {
      a[i + 1].push_back(A[i][j]);
    }
  }
  vector<long long> u(n + 1), v(m + 1);
  vector<int> p(m + 1), way(m + 1);
  for (int i = 1; i <= n; ++i) {
    p[0] = i;
    int j0 = 0;
    vector<long long> minv(m + 1, 100LL * INF);
    vector<char> used(m + 1, false);
    do {
      used[j0] = true;
      int i0 = p[j0], j1;
      long long delta = 100LL * INF;
      for (int j = 1; j <= m; ++j)
        if (!used[j]) {
          long long cur = a[i0][j] - u[i0] - v[j];
          if (cur < minv[j]) minv[j] = cur, way[j] = j0;
          if (minv[j] < delta) delta = minv[j], j1 = j;
        }
      for (int j = 0; j <= m; ++j)
        if (used[j])
          u[p[j]] += delta, v[j] -= delta;
        else
          minv[j] -= delta;
      j0 = j1;
    } while (p[j0] != 0);
    do {
      int j1 = way[j0];
      p[j0] = p[j1];
      j0 = j1;
    } while (j0);
  }
  vector<int> rv(n);
  for (int j = 1; j <= m; ++j) {
    rv[p[j] - 1] = j - 1;
  }
  return rv;
}
struct MinCostFlow {
  struct edge {
    int b, u, c, f;
    size_t back;
  };
  int n, m;
  vector<vector<edge> > g;
  MinCostFlow(int n) : n(n), m(0), g(n) {}
  void add_edge(int a, int b, int u, int c) {
    ++m;
    edge r1 = {b, u, c, 0, g[b].size()};
    edge r2 = {a, 0, -c, 0, g[a].size()};
    g[a].push_back(r1);
    g[b].push_back(r2);
  }
  int flow(int s, int t, int k) {
    int flow = 0, cost = 0;
    while (flow < k) {
      vector<int> id(n, 0);
      vector<int> d(n, INF);
      vector<int> q(n);
      vector<int> p(n);
      vector<size_t> p_edge(n);
      int qh = 0, qt = 0;
      q[qt++] = s;
      d[s] = 0;
      while (qh != qt) {
        int v = q[qh++];
        id[v] = 2;
        if (qh == n) qh = 0;
        for (size_t i = 0; i < g[v].size(); ++i) {
          edge &r = g[v][i];
          if (r.f < r.u && d[v] + r.c < d[r.b]) {
            d[r.b] = d[v] + r.c;
            if (id[r.b] == 0) {
              q[qt++] = r.b;
              if (qt == n) qt = 0;
            } else if (id[r.b] == 2) {
              if (--qh == -1) qh = n - 1;
              q[qh] = r.b;
            }
            id[r.b] = 1;
            p[r.b] = v;
            p_edge[r.b] = i;
          }
        }
      }
      if (d[t] == INF) break;
      int addflow = k - flow;
      for (int v = t; v != s; v = p[v]) {
        int pv = p[v];
        size_t pr = p_edge[v];
        addflow = min(addflow, g[pv][pr].u - g[pv][pr].f);
      }
      for (int v = t; v != s; v = p[v]) {
        int pv = p[v];
        size_t pr = p_edge[v], r = g[pv][pr].back;
        g[pv][pr].f += addflow;
        g[v][r].f -= addflow;
        cost += g[pv][pr].c * addflow;
      }
      flow += addflow;
    }
    if (flow < k) {
      return -1;
    }
    return cost;
  }
};
const int MAXN = 1024;
struct Dinic {
  struct edge {
    int a, b, cap, flow;
  };
  int n, s, t, d[MAXN], ptr[MAXN], q[MAXN];
  vector<edge> e;
  vector<int> g[MAXN];
  Dinic(int n) : n(n) {}
  void add_edge(int a, int b, int cap) {
    edge e1 = {a, b, cap, 0};
    edge e2 = {b, a, 0, 0};
    g[a].push_back((int)e.size());
    e.push_back(e1);
    g[b].push_back((int)e.size());
    e.push_back(e2);
  }
  bool bfs() {
    int qh = 0, qt = 0;
    q[qt++] = s;
    memset(d, -1, n * sizeof d[0]);
    d[s] = 0;
    while (qh < qt && d[t] == -1) {
      int v = q[qh++];
      for (size_t i = 0; i < g[v].size(); ++i) {
        int id = g[v][i], to = e[id].b;
        if (d[to] == -1 && e[id].flow < e[id].cap) {
          q[qt++] = to;
          d[to] = d[v] + 1;
        }
      }
    }
    return d[t] != -1;
  }
  int dfs(int v, int flow) {
    if (!flow) return 0;
    if (v == t) return flow;
    for (; ptr[v] < (int)g[v].size(); ++ptr[v]) {
      int id = g[v][ptr[v]], to = e[id].b;
      if (d[to] != d[v] + 1) continue;
      int pushed = dfs(to, min(flow, e[id].cap - e[id].flow));
      if (pushed) {
        e[id].flow += pushed;
        e[id ^ 1].flow -= pushed;
        return pushed;
      }
    }
    return 0;
  }
  int flow(int S, int T) {
    s = S;
    t = T;
    int flow = 0;
    for (;;) {
      if (!bfs()) break;
      memset(ptr, 0, n * sizeof ptr[0]);
      while (int pushed = dfs(s, INF)) flow += pushed;
    }
    return flow;
  }
};
struct MaxFlow {
  struct Edge {
    int to, c, ne;
    Edge(int to, int c, int ne) : to(to), c(c), ne(ne) {}
  };
  int n;
  vector<Edge> ed;
  vector<int> fi;
  MaxFlow(int n) : n(n), ed(), fi(n, -1) {}
  void add_edge(int a, int b, int c) {
    ed.push_back(Edge(b, c, fi[a]));
    fi[a] = (int)ed.size() - 1;
    ed.push_back(Edge(a, c, fi[b]));
    fi[b] = (int)ed.size() - 1;
  }
  vector<char> us;
  int dfs(int v, int tar, int cur, int minv = 1) {
    if (v == tar) return cur;
    if (us[v]) return 0;
    us[v] = 1;
    for (int i = fi[v]; i != -1; i = ed[i].ne) {
      if (ed[i].c < minv) {
        continue;
      }
      int tmp = dfs(ed[i].to, tar, min(cur, ed[i].c), minv);
      if (tmp > 0) {
        ed[i].c -= tmp;
        ed[i ^ 1].c += tmp;
        return tmp;
      }
    }
    return 0;
  }
  int flow(int s, int t) {
    int ans = 0, cur, mv = 1;
    for (int i = 0; i < 2; ++i) {
      do {
        us = vector<char>(n);
        cur = dfs(s, t, INF, mv);
        ans += cur;
      } while (cur);
    }
    return ans;
  }
};
struct BoundedMinFlow {
  vector<int> a, b;
  vector<int> l, r;
  int n;
  BoundedMinFlow(int n) : n(n) {}
  void add_edge(int f, int t, int minc, int maxc) {
    a.push_back(f);
    b.push_back(t);
    l.push_back(minc);
    r.push_back(maxc);
  }
  bool check(int s, int t, int m) {
    MaxFlow f(n + 2);
    f.add_edge(t, s, m);
    int total = 0;
    for (int i = 0; i < (int)a.size(); ++i) {
      if (l[i] > 0) {
        f.add_edge(n, b[i], l[i]);
        f.add_edge(a[i], n + 1, l[i]);
        total += l[i];
      }
      if (r[i] > l[i]) {
        f.add_edge(a[i], b[i], r[i] - l[i]);
      }
    }
    return (f.flow(n, n + 1) == total);
  }
  int flow(int s, int t) {
    int le = -1, ri = 10000;
    if (!check(s, t, ri)) {
      return -1;
    }
    while (le + 1 < ri) {
      int mi = (le + ri);
      if (check(s, t, mi)) {
        ri = mi;
      } else {
        le = mi;
      }
    }
    return ri;
  }
};
int bc(int x) {
  if (!x) {
    return 0;
  }
  return (x & 1) + bc(x >> 1);
}
int n, m;
int x[1024];
char let[1024];
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &x[i]);
  }
  vector<vector<int> > a(n + m);
  for (int i = 0; i < n + m; ++i) {
    a[i].resize(n + m);
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (j <= i) {
        a[i][j] = INF;
      } else {
        if (x[i] == x[j]) {
          a[i][j] = 0;
        } else {
          a[i][j] = bc(x[j]);
        }
      }
    }
    for (int j = 0; j < m; ++j) {
      a[i][j + n] = 0;
    }
  }
  for (int i = 0; i < m; ++i) {
    for (int j = 0; j < n; ++j) {
      a[i + n][j] = bc(x[j]);
    }
    for (int j = 0; j < m; ++j) {
      a[i + n][j + n] = 0;
    }
  }
  vector<int> to = hung(a);
  vector<int> from(n + m);
  for (int i = 0; i < (int)to.size(); ++i) {
    from[to[i]] = i;
  }
  for (int i = 0; i < m; ++i) {
    let[n + i] = 'a' + i;
  }
  int pen = 0;
  int cnt = 0;
  for (int i = 0; i < n; ++i) {
    int pr = from[i];
    let[i] = let[pr];
    if (pr >= n || x[pr] != x[i]) {
      ++cnt;
      pen += bc(x[i]);
    }
    ++cnt;
  }
  printf("%d %d\n", cnt, pen);
  for (int i = 0; i < n; ++i) {
    int pr = from[i];
    let[i] = let[pr];
    if (pr >= n || x[pr] != x[i]) {
      pen += bc(x[i]);
      printf("%c=%d\n", let[i], x[i]);
    }
    printf("print(%c)\n", let[i]);
  }
  return 0;
}