A directed acyclic graph consists of $n$ nodes and $m$ edges. The nodes are numbered $1,2,\dots,n$ .

Calculate for each node the number of nodes you can reach from that node (including the node itself).

The first input line has two integers $n$ and $m$ : the number of nodes and edges.

Then there are $m$ lines describing the edges. Each line has two distinct integers $a$ and $b$ : there is an edge from node $a$ to node $b$ .

• $1 \le n \le 5 \cdot 10^4$
• $1 \le m \le 10^5$

Print $n$ integers: for each node the number of reachable nodes.