Where am I?

Grandpa Marat resides in a distant city known as C. He enjoys visiting friends, often spending several days traveling from one friend's house to another. When leaving a house, he only visits friends of the current hosts. Grandpa Marat may visit some friends multiple times and might even return home to enjoy tea with his grandchildren. However, due to his forgetfulness, he sometimes fails to return home. His grandchildren, concerned for his safety, always track him down and bring him back. Over time, they have noticed that before they find him, Grandpa Marat visits exactly (k) friends (including his grandchildren).

Recently, Grandpa Marat went on another visit, and his grandchildren are eager to know where he might be found. Help them determine his possible locations.

Input

The first line of the input contains three integers (n), (m), and (k), where (n) is the number of houses in city C, (m) is the number of pairs of friends ((1 $\le$ n $\le$ 1000), (1 $\le$ m $\le$ 200000), (1 $\le$ k $\le$ 10^9)).

The following (m) lines each describe a pair of friends with two integers, representing the house numbers of the friends. If the owners of house (i) are friends with the owners of house (j), then the owners of house (j) are also friends with the owners of house (i).

Grandpa Marat and his grandchildren reside in house number (1).

Output

The first line of the output should contain the integer (p) - the number of houses where Grandpa Marat could potentially be. The second line should list (p) integers - the house numbers where Grandpa Marat might be found, sorted in ascending order.

Examples