Problem:
Score : 500 points

Problem Statement

Rng has a connected undirected graph with N vertices.
Currently, there are M edges in the graph, and the i-th edge connects Vertices A_i and B_i.

Rng will add new edges to the graph by repeating the following operation:

Operation: Choose u and v (u \neq v) such that Vertex v can be reached by traversing exactly three edges from Vertex u, and add an edge connecting Vertices u and v. It is not allowed to add an edge if there is already an edge connecting Vertices u and v.

Find the maximum possible number of edges that can be added.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N

The graph has no self-loops or multiple edges.

The graph is connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find the maximum possible number of edges that can be added.

Sample Input 1

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 1

4

If we add edges as shown below, four edges can be added, and no more.

Sample Input 2

5 5
1 2
2 3
3 1
5 4
5 1

Sample Output 2

5

Five edges can be added, for example, as follows:

Add an edge connecting Vertex 5 and Vertex 3.

Add an edge connecting Vertex 5 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 1.

Add an edge connecting Vertex 4 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 3.

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

//set many funcs
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#define inf 1072114514
#define llinf 1145141919810364364
#define mod 1000000007

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}

typedef struct{
long long a;
long long b;
}data;
 
int sortfnc(const void *a,const void *b){
if(((data*)a)->a == ((data*)b)->a){return 0;}
if(((data*)a)->a < ((data*)b)->a){return -1;}
return 1;
}

long long lib[131072]={0},q[131072],qpi=0,qpo=0;

void makelib(data x[],long long m){
    int i;
    for(i=1;i<m;i++){if(x[i-1].a!=x[i].a){lib[x[i].a]=i;}}
}

void qpush(long long x){
    q[qpi]=x;qpi++;
}

long long qpop(){
    qpo++;
    return q[qpo-1];
}

int main(void){
    long long co,n,m,i,c[131072]={0},a,b,p,fl=0;
    data dat[262144];
    scanf("%lld%lld",&n,&m);co=n;
    for(i=0;i<m;i++){
        scanf("%lld%lld",&a,&b);
        dat[2*i].a=a;dat[2*i].b=b;
        dat[2*i+1].a=b;dat[2*i+1].b=a;
    }
    qsort(dat,2*m,sizeof(data),sortfnc);
    makelib(dat,2*m);
    c[1]=1;lib[n+1]=2*m;
    qpush(1);
    while(co){
        p=qpop();co--;
        //printf("%lld %lld %lld\n",p,c[p],fl);
        for(i=lib[p];i<lib[p+1];i++){
            //printf("[%lld|%lld]",dat[i].b,c[dat[i].b]);
            if(c[dat[i].b] == 0){
                c[dat[i].b]=3-c[p];qpush(dat[i].b);
            }
            else if(c[dat[i].b] == c[p]){fl=1;break;}
        }
        //printf("\n");
    }
    if(fl==1){printf("%lld\n",llnCr(n,2)-m);}
    else{printf("%lld\n",(n/2)*llceil(n,2)-m);}
    return 0;
}