Codeforces Round #346 (Div. 2) C模拟

C. Tanya and Toys

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

In Berland recently a new collection of toys went on sale. This collection consists of 109 types of toys, numbered with integers from 1 to109. A toy from the new collection of the i-th type costs i bourles.

Tania has managed to collect n different types of toys a1, a2, ..., an from the new collection. Today is Tanya's birthday, and her mother decided to spend no more than m bourles on the gift to the daughter. Tanya will choose several different types of toys from the new collection as a gift. Of course, she does not want to get a type of toy which she already has.

Tanya wants to have as many distinct types of toys in her collection as possible as the result. The new collection is too diverse, and Tanya is too little, so she asks you to help her in this.

Input

The first line contains two integers n (1 ≤ n ≤ 100 000) and m (1 ≤ m ≤ 109) — the number of types of toys that Tanya already has and the number of bourles that her mom is willing to spend on buying new toys.

The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the types of toys that Tanya already has.

Output

In the first line print a single integer k — the number of different types of toys that Tanya should choose so that the number of different types of toys in her collection is maximum possible. Of course, the total cost of the selected toys should not exceed m.

In the second line print k distinct space-separated integers t1, t2, ..., tk (1 ≤ ti ≤ 109) — the types of toys that Tanya should choose.

If there are multiple answers, you may print any of them. Values of ti can be printed in any order.

Examples

input

3 71 3 4

output

22 5 

input

4 144 6 12 8

output

47 2 3 1

Note

In the first sample mom should buy two toys: one toy of the 2-nd type and one toy of the 5-th type. At any other purchase for 7 bourles (assuming that the toys of types 1, 3 and 4 have already been bought), it is impossible to buy two and more toys.

题意：一开始把题目想复杂了，(可能是因为最近做背包做多了)，把题意看成得到的玩具的数量最多而且总价钱最大在不超出m情况下，后面问人才知道，只有保证玩具的数量最多就可以了，大水题~~；

思路：模拟大法好；

代码：

#include<cstdio>  #include<cstring>#include <algorithm>#include <cmath>using namespace std;  #define maxn 111111#define inf 0x3f3f3f3ftypedef long long ll;int b[maxn],a[maxn];int main()  {  #ifdef CDZSC_Junefreopen("t.txt", "r", stdin);  //freopen("E:\\w.txt", "w", stdout); #endif  int n,m,sum,cnt,p;while(~scanf("%d%d",&n,&m)){for(int i = 0; i<n; i++){scanf("%d",&a[i]);}sort(a,a+n);p =cnt = sum = 0;for(int i = 1; ;i++){if(a[p] == i && p < n){p++;continue;}if(sum + i > m)break;b[cnt++] = i;sum += i;}printf("%d\n",cnt);if(cnt!= 0){printf("%d",b[0]);for(int i = 1;i<cnt;i++){printf(" %d",b[i]);}puts("");}}return 0;  }