Gym

B

Although Haneen was able to solve the LCS problem, Dr. Ibrahim is suspicious about whether she really understands the LCS problem or not. He believes that she can't write the code on her own, but can only translate the LCS pseudo-code given in class into C++ code without really understanding how it works. Here is the pseudo-code Dr. Ibrahim gave in class:

function LCS (A[1..R], B[1..C])
    DP = array(0..R, 0..C)
    for i := 0..R
       DP[i,0] = 0
    for j := 0..C
       DP[0,j] = 0
    for i := 1..R
        for j := 1..C
            if A[i] = B[j]
                DP[i,j] := DP[i-1,j-1] + 1
            else
                DP[i,j] := max(DP[i,j-1], DP[i-1,j])
    return DP[R,C]

To verify that Haneen understands the LCS problem, Dr. Ibrahim asked her to solve the following problem:

After running the above LCS code on two strings A and B, the 2D array DP is filled with values. Given the 2D array DP, can you guess what A and B are? Any two strings A and B that will produce the given table and contain only lowercase English letters are acceptable.

Can you help Haneen solve this problem?

Input

The first line of input contains two integers R and C (1 ≤ R, C ≤ 25), the length of the strings A and B, respectively.

Each of the following R + 1 lines contains C + 1 integers, these lines represent the 2D array DP.

It's guaranteed that the given table was produced by running the algorithm on two strings that contain only lowercase English letters.

Output

Print string A on the first line and string B on the second line. Both strings should contain only lowercase English letters.

Example

Input

3 4
0 0 0 0 0
0 0 1 1 1
0 0 1 1 2
0 1 1 1 2

Output

abc
cadb
把所有联通的点公用一个字母，注意多对多的字母相等关系。
长度为25，即a-x,所以其他不联通的点都为z

#include <iostream>
#include <string>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <stack>
#include <iomanip>
#include <vector>
#include <set>
#include <map>
#include <deque>
#include <list>
#include <bitset>

using namespace std;

typedef long long ll;
const int MAXN = 1005;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;

int n, m, dp[55][55];
char a[50], b[50];
int main()
{
    cin >> n >> m;
    int i, j, k;
    for(i = 0;i <= n;++i)
        for(j = 0;j <= m;++j)
        cin >> dp[i][j];
    for(i = 1;i < 30;++i)
        a[i] = 'a' - 1 + i;
    for(i = 1;i <= n;++i)
        for(j = 1;j <= m;++j)
        {
            if(dp[i][j] != max(dp[i - 1][j], dp[i][j - 1]))
            {
                if(b[j])
                {
                    for(k = 1;k <= m;++k)
                        if(b[k] == a[i])
                        b[k] = b[j];
                    //把之前与 a[i] 相同的字母都换，所以参考字母 a[i] 不能换
                    for(k = 1;k <= n;++k)
                        if(a[i] == a[k] && k != i)
                        a[k] = b[j];
                    a[i] = b[j];
                }
                else
                    b[j] = a[i];
            }
        }

    for(i = 1;i <= m;++i)
        if(!b[i])
        b[i] = 'z';

    a[n + 1] = b[m + 1] = 0;
    cout << (a + 1) << endl << (b + 1) << endl;
    return 0;
}

 ------------------------------------------

D

 

In this cafeteria, the N tables are all ordered in one line, where table number 1 is the closest to the window and table number N is the closest to the door.

 

Each time a group of X people enter the cafeteria, one of the cafeteria staff escorts the guests to the table with the smallest number of chairs greater than or equal to X chairs among all available tables. If there’s more than one such table, the guests are escorted to the table that is closest to the window. If there isn't any suitable table available, the group will leave the cafeteria immediately. A table is considered available if no one sits around it.

 

Eyad likes to help others and also likes to prove that he has learned something from the training of Master Hasan. Therefore, he decided to write a program that helps the cafeteria staff choose the right table for a newly arriving group.

 

Given the log file of who entered and who left the cafeteria, find the table at which a given group should sit.

 

Input

 

The first line of input contains two integers N and Q (1 ≤ N, Q ≤ 10⁵), the number of tables in the cafeteria and the number of events in the log file.

 

The second line contains N integers, each represents the size of a table (number of chairs around it). The tables are given in order from 1 to N. The size of each table is at least 1 and at most 10⁵.

 

Each of the following Q lines describes an event in one of the following formats:

 

- in X: means a group of X (1 ≤ X ≤ 10⁵) people entered the cafeteria.

 

- out T: means the group on table number T (1 ≤ T ≤ N) just left the cafeteria, the table is now available. It is guaranteed that a group was sitting on this table (input is valid).

 

Initially, all tables are empty, and the log lists the events in the same order they occurred (in chronological order).

 

Output

 

For each event of the first type, print the number of the table on which the coming group should sit. If for any event a group cannot be escorted to any table, print  - 1 for that event.

 

Example

 

Input

4 7
1 2 6 7
in 4
in 1
in 3
in 5
out 1
out 4
in 7

Output

3
1
4
-1
4
-------------------------------------------------
不用 set ，二分可以试试
lower_bound()返回一个 iterator 它指向在[first,last)标记的有序序列中可以插入value，而不会破坏容器顺序的第一个位置，而这个位置标记了一个不小于value 的值

^[1]

  。该函数为C++ STL内的函数。
——百度百科

 1 #include <iostream>
 2 #include <cstring>
 3 #include <cmath>
 4 #include <cstdio>
 5 #include <iomanip>
 6 #include <string>
 7 #include <set>
 8 #include <queue>
 9 #include <stack>
10 #include <map>
11 #include <algorithm>
12 
13 using namespace std;
14 
15 typedef long long LL;
16 const int INF = 0x3f3f3f3f;
17 const int MAXN = 100005;
18 const int MOD = 1e9+7;
19 
20 int main()
21 {
22     int n, Q;
23     cin >> n >> Q;
24     int desk[MAXN];
25     set<pair<int, int> > s;
26     set<pair<int, int> > :: iterator it;
27     for(int i = 1;i <= n;++i)
28     {
29         cin >> desk[i];
30         s.insert(make_pair(desk[i], i));
31     }
32     string str;
33     int t;
34     while(Q--)
35     {
36         cin >> str >> t;
37         if(str[0] == 'i')
38         {
39             it = s.lower_bound(make_pair(t, 0));
40             if(it == s.end())
41                 cout << -1 << endl;
42             else
43             {
44                 cout << it -> second << endl;
45                 s.erase(it);
46             }
47         }
48         else
49             s.insert(make_pair(desk[t], t));
50     }
51     return 0;
52 }

 

 

-------------------------------------------

G

 

There are K hours left before Agent Mahone leaves Amman! Hammouri doesn't like how things are going in the mission and he doesn't want to fail again. Some places have too many students covering them, while other places have only few students.

Whenever Hammouri commands a student to change his place, it takes the student exactly one hour to reach the new place. Hammouri waits until he is sure that the student has arrived to the new place before he issues a new command. Therefore, only one student can change his place in each hour.

Hammouri wants to command the students to change their places such that after K hours, the maximum number of students covering the same place is minimized.

Given the number of students covering each place, your task is to find the maximum number of students covering the same place after K hours, assuming that Hammouri correctly minimizes this number.

Input

The first line of input contains two integers M (2 ≤ M ≤ 10⁵) and K (1 ≤ K ≤ 10⁹), where M is the number of places and K is the number of hours left before Agent Mahone leaves Amman.

The second line contains M non-negative integers, each represents the number of students covering one of the places. Each place is covered by at most 10⁹ students.

Output

Print the maximum number of students covering a place after K hours, assuming that Hammouri minimized this number as much as possible in the last K hours.

Examples

Input

5 4
3 4 1 4 9

Output

5

Input

2 1000000000
1000000000 4

Output

500000002

Input

5 3
2 2 2 2 1

Output

2
---------------------------------------
二分，注意边界
刚开始，以平均值和最大值为边界，计算可移动的数目小于题目所给值即可

 1 #include <iostream>
 2 #include <cstring>
 3 #include <cmath>
 4 #include <cstdio>
 5 #include <iomanip>
 6 #include <string>
 7 #include <set>
 8 #include <queue>
 9 #include <stack>
10 #include <map>
11 #include <algorithm>
12 
13 using namespace std;
14 
15 typedef long long LL;
16 const int INF = 0x3f3f3f3f;
17 const int MAXN = 100005;
18 const int MOD = 1e9+7;
19 
20 int main()
21 {
22     int n, i;
23     LL k, num[MAXN], mx = 0, sum = 0;
24     cin >> n >> k;
25     for(i = 0;i < n;++i)
26     {
27         cin >> num[i];
28         mx = max(mx, num[i]);
29         sum += num[i];
30     }
31 //    int ave = mx / m;
32 //    if(mx % m)
33 //        ave++;
34 //    等同于下行码
35     LL ave = (sum + n - 1) / n;
36     LL l = ave, r = mx, mid, ans;
37     while(l <= r)
38     {
39         mid = (l + r) >> 1;
40         sum = 0;
41         for(i = 0;i < n;++i)
42             if(num[i] > mid)
43             sum += (num[i] - mid);
44         if(sum <= k)
45         {
46             ans = mid;
47             r = mid - 1;
48         }
49         else
50             l = mid + 1;
51 //        cout << sum << endl;
52     }
53     cout << ans << endl;
54     return 0;
55 }

------------------------------------------------------------------

M

George met AbdelKader in the corridor of the CS department busy trying to fix a group of incorrect equations. Seeing how fast he is, George decided to challenge AbdelKader with a very large incorrect equation. AbdelKader happily accepted the challenge!

Input

The first line of input contains an integer N (2 ≤ N ≤ 300), the number of terms in the equation.

The second line contains N integers separated by a plus + or a minus -, each value is between 1 and 300.

Values and operators are separated by a single space.

Output

If it is impossible to make the equation correct by replacing operators, print  - 1, otherwise print the minimum number of needed changes.

Examples

Input

7
1 + 1 - 4 - 4 - 4 - 2 - 2

Output

3

Input

3
5 + 3 - 7

Output

-1

 1 #include <iostream>
 2 #include <string>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <iomanip>
 7 #include <stack>
 8 #include <queue>
 9 #include <set>
10 #include <map>
11 
12 using namespace std;
13 
14 typedef long long LL;
15 const int MAXN = 100005;
16 const int INF = 0x3f3f3f3f;
17 const int MOD = 1e9 + 7;
18 
19 #define Mem0(x) memset(x, 0, sizeof(x));
20 #define MemM(x) memset(x, 0x3f, sizeof(x));
21 //01背包，第 i 个物品剩余容量为 j 时操作次数
22 int n, a[305], dp[305][180005], sum;
23 int main()
24 {
25     cin >> n >> a[1];
26     sum = a[1];
27     int i, j;
28     char c;
29     for(i = 2;i <= n;++i)
30     {
31         cin >> c >> a[i];
32         sum += a[i];
33         if(c == '-')
34             a[i] = - a[i];
35     }
36     if(sum % 2)
37         cout << -1 << endl;
38     else
39     {
40         MemM(dp);
41         dp[1][sum / 2 + a[1]] = 0;
42         for(i = 2;i <= n;++i)
43             for(j = 0;j <= sum;++j)
44             {
45                 if(j >= a[i])
46                     dp[i][j] = min(dp[i][j], dp[i - 1][j - a[i]]);
47                 if(j >= -a[i])
48                     dp[i][j] = min(dp[i][j], dp[i - 1][j + a[i]] + 1);
49             }
50 
51 //        cout << endl;
52 //        for(i = 1;i <= n;++i)
53 //        {
54 //            for(j = 0;j <= sum;++j)
55 //                cout << dp[i][j] << " ";
56 //            cout << endl;
57 //        }
58 
59         if(dp[n][sum / 2] >= n)
60              cout << -1 << endl;
61         else
62             cout << dp[n][sum / 2] << endl;
63     }
64     return 0;
65 }