13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T60b,

You are given a cactus graph, in this graph each edge lies on at most one simple cycle.

It is given as $$$m$$$ edges $$$a_i, b_i$$$, weight of $$$i$$$-th edge is $$$i$$$.

Let's call a path in cactus increasing if the weights of edges on this path are increasing.

Let's call a pair of vertices $$$(u,v)$$$ happy if there exists an increasing path that starts in $$$u$$$ and ends in $$$v$$$.

For each vertex $$$u$$$ find the number of other vertices $$$v$$$, such that pair $$$(u,v)$$$ is happy.

Input

The first line of input contains two integers $$$n,m$$$ ($$$1 \leq n, m \leq 500\,000$$$): the number of vertices and edges in the given cactus.

The next $$$m$$$ lines contain a description of cactus edges, $$$i$$$-th of them contain two integers $$$a_i, b_i$$$ ($$$1 \leq a_i, b_i \leq n, a_i \neq b_i$$$).

It is guaranteed that there are no multiple edges and the graph is connected.

Happy Cactus

Examples