Problem:
Score : 600 points

Problem Statement

You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1.
The edges are given in the format (x_i,y_i), which means that Vertex x_i and y_i are connected by an edge.

Each vertex i has a value a_i.
You want to add edges in the given forest so that the forest becomes connected.
To add an edge, you choose two different vertices i and j, then span an edge between i and j.
This operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.

Find the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Constraints

1 ≤ N ≤ 100,000

0 ≤ M ≤ N-1

1 ≤ a_i ≤ 10^9

0 ≤ x_i,y_i ≤ N-1

The given graph is a forest.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M
a_0 a_1 .. a_{N-1}
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Sample Input 1

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6

Sample Output 1

7

If we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.

Sample Input 2

5 0
3 1 4 1 5

Sample Output 2

Impossible

We can't make the graph connected.

Sample Input 3

1 0
5

Sample Output 3

0

The graph is already connected, so we do not need to add any edges.

Solution in C (GCC 9.2.1) (judge verdict: Runtime Error)

#pragma region kyopuro_templates
#pragma GCC optimize("Ofast")
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<stdbool.h>
#include<assert.h>
#include<time.h>
#include<ctype.h>
typedef long long ll;
typedef long double ld;
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))
#define rrep(i,l,r)for(ll i=(l);i>=(r);i--)
#define INF (1LL<<62)
#define MOD1 1000000007
#define MOD2 998244353
#define MAX_N (1 << 20)
#define YES printf("Yes\n")
#define NO printf("No\n")
#define PN printf("\n")
#define charsize 100005 //10^5+5
#define PI 3.141592653589793238

void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a= c;}
void cin(ll *n){ scanf("%lld",&(*n)); }
ll max2(ll a,ll b){return a>=b?a:b;}
ll min2(ll a,ll b){return a>=b?b:a;}
ll min3(ll a, ll b, ll c){return (a<=b && a<=c) ? a : b<=c ? b : c;}
ll max3(ll a, ll b, ll c){return (a>=b && a>=c) ? a : b>=c ? b : c;}
ll minn(ll n, ll a[]){ll b=INF;rep(i,0,n) b=min2(b,a[i]);return b;}
ll maxn(ll n, ll a[]){ll b=-INF;rep(i,0,n) b=max2(b,a[i]);return b;}
ll POW(ll a, ll b){ll c=1;rep(i,0,b) c*=a;return c;}
double POW_d(double a, double b){double c=1;rep(i,0,b) c*=a;return c;}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
ll mod_MOD1(ll n){n+= n<0?((-n)/MOD1+1)*MOD1:0; return n%=MOD1;}
ll mod_p(ll n ,ll p){n+= n<0?((-n)/p+1)*p:0; return n%=p;}
ll change_into_num(char s[] , ll len, ll p){ return !p ? 0 : POW(10,p-1)*(s[len-p]-'0') + change_into_num(s,len,p-1); }
ll digits(ll a, ll b){return a/b?1+digits(a/b,b):1;}
ll base(ll n, ll a, ll i){return i==1?n%a:base(n/a,a,i-1);}
ll is_inArr1(ll x, ll n){ return ( x<0 || x>=n ) ? 0 : 1 ; }
ll is_inArr2(ll y, ll x, ll h, ll w){ return ( y<0 || y>=h || x<0 || x>=w ) ? 0 : 1 ; }


void lr_lower( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am < val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am <= val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
void lr_upper( int *l, int *r, ll am, ll val , int type ){ (type<3) ? ( am <= val ?  ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ) : ( am < val ? ( *l = (*l+*r)/2 ) : ( *r= (*l+*r)/2 ) ); }
int cmp_lower( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a>=b ? 1 : 0 ) : ( a>b ? 1 : 0 ) ; }
int cmp_upper( ll a, ll b, int type ){ return (type==1) ? ( a==b ? 1 : 0 ) : (type==2) ? ( a<=b ? 1 : 0 ) : ( a<b ? 1 : 0 ) ; }
// return smallest p  which meets  a[p]==val :1  >=:2   >:3
ll lower_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_lower(&l,&r,a[ (l+r)/2 ],val,type);  return cmp_lower(a[l],val,type) ? l : cmp_lower(a[r],val,type) ? r : -1;  }
// return biggest p  which meets   a[p]==val :1  <=:2   <:3
ll upper_bound( ll a[], int l, int r, ll val , int type ){  while(r-l>1) lr_upper(&l,&r,a[ (l+r)/2 ],val,type); return cmp_upper(a[r],val,type) ? r : cmp_upper(a[l],val,type) ? l : -1; }
// count i  which meets ai==x
ll count(ll a[], int l, int r, ll x){  int p = lower_bound(a,l,r,x,1);  return p==-1 ? 0 : upper_bound(a,p,r,x,1)-p+1; }

ll *factors[2] , fac_cnt=0 , is_factor_prepared=0;
ll factor_pre(){  rep(i,0,1){ if(is_factor_prepared++) return 0; }  ll tmp=(1e6)/2+1, fac_tmp[tmp];  rep(i,0,tmp){fac_tmp[i]=i?2*i+1:2;}  rep(i,1,tmp){if(fac_tmp[i]){  repp(j,3,tmp/(2*i+1)+1,2 ){  if( j*(2*i+1)<tmp ) fac_tmp[ (j*(2*i+1)-1)/2 ]=0;  }  }else continue;}  rep(i,0,tmp){if(fac_tmp[i]){  rep(j,0,2){ factors[j] = realloc( factors[j] , sizeof(ll)*( fac_cnt +1 ) );  factors[j][j?fac_cnt++:fac_cnt]=j?0:fac_tmp[i];  }  } }  return 0;  }
ll factor(ll n, ll new_common_plus){ factor_pre();  rep(i,0,fac_cnt){ ll cnt=0; rep(j,0,1){ while( ( cnt+= n %factors[0][i]==0 ? 1 : 0 )  && (n/=factors[0][i]) %factors[0][i]==0 ) continue; } factors[1][i]= new_common_plus==1 ? cnt :  new_common_plus==2 ? max2(factors[1][i],cnt) : factors[1][i]+cnt ;  if( factors[0][i]> n ) break; } return n; }
ll judge_prime(ll n){ factor_pre(); rep(i,0,fac_cnt){ if(n<factors[0][i]*factors[0][i] || n==factors[0][i]) break; else if(n%factors[0][i]==0) n/=n; }  return n==1?0:1; }

ll *mf_arr,*inv_arr,*finv_arr,is_minv_made=0,is_mf_made=0,num_of_inv=2*1e6+10;
ll makeinv(ll n , ll mod){  rep(i,0,1){if(is_minv_made++) return 0;}  inv_arr = realloc(inv_arr, sizeof(ll)*2 );  finv_arr = realloc(finv_arr, sizeof(ll)*2 );  inv_arr[1]=1;finv_arr[0]=finv_arr[1]=1;  rep(i,2,n+1){  inv_arr = realloc(inv_arr, sizeof(ll)*(i+1) );  finv_arr = realloc(finv_arr, sizeof(ll)*(i+1) );  inv_arr[i]= mod - inv_arr[mod%i] * (mod / i) % mod;  finv_arr[i] = finv_arr[i - 1] * inv_arr[i] % mod;  }  return 0; }
ll make_mf(ll n, ll mod){  rep(i,0,1){ if(is_mf_made++) return 0; }  mf_arr = realloc(mf_arr, sizeof(ll)*2 );  ll x=1;  mf_arr[0]=mf_arr[1]=x;  rep(i,2,n+1){   x=x*i%mod;  mf_arr = realloc(mf_arr, sizeof(ll)*(i+1) );  mf_arr[i]=x; }  return 0;  }
ll m_inv(ll x, ll mod, ll is_fac ){ makeinv(num_of_inv,mod);  return is_fac?finv_arr[x]:inv_arr[x]; }
ll m_f(ll x, ll mod){  make_mf(num_of_inv,mod);  return mf_arr[x];  }
ll mod_nck(ll n, ll k, ll mod){ return m_f(n,mod)*m_inv(k,mod,1)%mod*m_inv(n-k,mod,1)%mod; }
ll m_p(ll r,ll n,ll mod){  ll t=1,s=r;  while(n>0){ t = (n&1) ? t*s%mod : t;  s=s*s%mod; n>>=1; }  return r?t:0;  }
ll m_mul2(ll a, ll b, ll mod){ return a*b%mod; }
ll m_mul3(ll a, ll b, ll c, ll mod){ return m_mul2(a*b%mod,c,mod); }
ll m_mul4(ll a, ll b, ll c, ll d, ll mod){ return m_mul3(a*b%mod,c,d,mod); }
ll m_mul5(ll a, ll b, ll c, ll d, ll e, ll mod){ return m_mul4(a*b%mod,c,d,e,mod); }

int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
int downll(const void*a, const void*b){return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;}
int cmp_string( const void * a , const void * b ) {  return strcmp( (char *)a , (char *)b ); }  // qsort((void*)s,n,sizeof(s[0]),int_sort );
int cmp_char(const void * a, const void * b) { return *(char *)a - *(char *)b;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}
void sortdown(ll*a,int n){qsort(a,n,sizeof(ll),downll);}
void sort_string(int n,int size,char s[][size]){ qsort( (void*)s , n , sizeof(s[0]) , cmp_string ); }
void sort_char(char *s){ qsort( (void *)s , strlen(s) , sizeof(char) , cmp_char ); }
ll unique_string(ll n ,ll size, char s[][size]){ ll ans=1; rep(i,1,n) if( strcmp(s[i],s[i-1]) ) ans++; return ans; }
ll unique_num(ll n , ll a[]){ ll ans=1; rep(i,1,n) if( a[i]!=a[i-1] ) ans++; return ans; }

ll compare(ll a, ll b){ return a<b?-1:a>b?1:0; }
typedef struct{ ll a , b;}fr;
int cmp1( const void *p, const void *q ){  
    ll pa=((fr*)p)->a; ll qa=((fr*)q)->a;  return compare(pa,qa);  
}
int cmp2( const void *p, const void *q ){
    ll pa=((fr*)p)->a; ll qa=((fr*)q)->a;  return compare(qa,pa);
}
void strsortup(fr*a,int n){qsort(a,n,sizeof(fr),cmp1);}
void strsortdown(fr*a,int n){qsort(a,n,sizeof(fr),cmp2);}

void sort_partial(ll a[],int begin,int end,int is_increase){
    ll *b;  b = (ll *) malloc( sizeof(ll)*(end-begin) );

    rep(i,begin,end) b[i-begin]=a[i];
    if(is_increase) sortup(b,end-begin); else sortdown(b,end-begin);
    rep(i,begin,end) a[i]=b[i-begin];
}


#pragma region AVL
/*---------------------------AVL start--------------------------------*/
//https://qiita.com/mikecat_mixc/items/e9f8248de2ae7f7a0a29
typedef struct node_AVL_set{  
    ll val;
    int diff;
    int cnt;
    struct node_AVL_set *child[2];
}AVL_set;
void AVL_set_inside_rotate(AVL_set **node, int is_right){
    int l = is_right==false , r = is_right==true , sign = is_right ? 1 : -1;
    if((*node)->child[l] != NULL){
        AVL_set* left = (*node)->child[l];
        int a= (*node)->diff * sign , b= left->diff * sign ,na,nb;
        if(b+1){
            na=a-1-b;
            nb= (a-b) ? b-1 : a-2;
        }else{
            na=a-1;
            nb= a ? b-1 : a+b-2;
        }
        (*node)->diff = na * sign;
        left->diff = nb * sign;
        /* rotate-> */
        (*node)->child[l] = (*node)->child[l]->child[r];
        left->child[r] = *node;
        *node = left;
    }
}
int AVL_set_inside_update(AVL_set **node, ll data, int add){
    if(*node == NULL){
        if(add==2){
            *node = malloc(sizeof(AVL_set));
            (*node)->val = data;
            (*node)->cnt = 1;
            (*node)->diff = 0;
            (*node)->child[0] = NULL;
            (*node)->child[1] = NULL;
        }
        return add==2 ? *node != NULL : 0; 
    }else{
        int l, delta, delta_sign; AVL_set *next_node;
        if(data == (*node)->val){
            if(add==2){
                (*node)->cnt++;
                return 0;
            }else{
                if( add && (*node)->cnt > 1 ){
                    (*node)->cnt--; return 0;
                }else{
                    if((*node)->child[1] == NULL){
                        next_node = (*node)->child[0];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else if((*node)->child[0] == NULL){
                        next_node = (*node)->child[1];
                        free(*node);
                        *node = next_node;
                        return -1;
                    }else{
                        for(next_node = (*node)->child[0];
                        next_node->child[1] != NULL;
                        next_node = next_node->child[1]);
                        (*node)->val = next_node->val;
                        l=0;
                        delta_sign=1;
                        delta = AVL_set_inside_update(&(*node)->child[l], next_node->val, add);
                    }
                }
            }
        }else{
            l = data >= (*node)->val ? 1 : 0;
            delta_sign = data < (*node)->val ? 1 : -1;
            delta = AVL_set_inside_update(&(*node)->child[l], data, add);
        }
        if( delta ){
            int orig_diff = (*node)->diff;
            int do_rotate = 0, rotate_l , diff_sign , rotate_right;
            (*node)->diff += delta * delta_sign;
            if((*node)->diff > 1){
                do_rotate = 1;
                rotate_l = 0;
                diff_sign = 1;
                rotate_right = 1;
            }else if((*node)->diff < -1){
                do_rotate = 1;
                rotate_l = 1;
                diff_sign = -1;
                rotate_right = 0;
            }
            if(do_rotate){
                int child_diff = (*node)->child[rotate_l]->diff;
                if((*node)->child[rotate_l]->diff * diff_sign < 0){
                    AVL_set_inside_rotate(&(*node)->child[rotate_l], !rotate_right);
                }
                AVL_set_inside_rotate(node, rotate_right);
                return delta < 0 && child_diff != 0 ? -1 : 0;
            }
            if     (delta > 0 && orig_diff == 0) return 1;
            else if(delta < 0 && orig_diff != 0) return -1;
            else                                 return 0;
        }else{ 
            return 0;
        }
    }
}

void AVL_set_inside_print(const AVL_set *node, int depth){
    if(node == NULL) return;
    AVL_set_inside_print(node->child[1], depth + 1);
    printf("%lld %d\n", node->val,node->cnt);
    AVL_set_inside_print(node->child[0], depth + 1);    
}
void AVL_set_inside_free(AVL_set *node){
    if(node == NULL) return;
    AVL_set_inside_free(node->child[0]);
    AVL_set_inside_free(node->child[1]);
    free(node);
}
ll AVL_set_inside_count(AVL_set *root, ll val){
    AVL_set *node; node = root;
    while(node){
        if     (val < node->val) node = node->child[0];
        else if(val > node->val) node = node->child[1];
        else                     return node->cnt;
    }
    return 0;
}
ll AVL_set_inside_minmax(AVL_set *root, int type){
    while(root->child[type] !=NULL)  root= root->child[type];
    return root->val;
}
void AVL_set_inside_swap(AVL_set **node1, AVL_set **node2){  
    AVL_set *tmp;  tmp=*node1; *node1=*node2; *node2=tmp;
}

#define set_MAX_SIZE 514511
ll set_main( int command , int set_num , ll val ){
    static bool set_is_init=false;
    static AVL_set *set_pointer[set_MAX_SIZE];
    static ll set_siz[set_MAX_SIZE];
    if(!set_is_init){ set_is_init=true; rep(i,0,set_MAX_SIZE){ *(set_pointer+i) = NULL; set_siz[i]=0; } }
    if(command==-1){ AVL_set_inside_print( set_pointer[set_num] ,0); }
    if(command==1){ AVL_set_inside_count(set_pointer[set_num],val) ? 1 : set_siz[set_num]++;  AVL_set_inside_update( &set_pointer[set_num] , val , 2 ); }
    if(command==2){ return AVL_set_inside_count(set_pointer[set_num],val); }
    if(command==3){ ( AVL_set_inside_count(set_pointer[set_num],val) > 1 ) ? 1 : set_siz[set_num]--;  AVL_set_inside_update( &set_pointer[set_num] , val,1); }
    if(command==4){ set_siz[set_num]--; AVL_set_inside_update( &set_pointer[set_num] , val , 0 ); }
    if(command==5){ set_siz[set_num]=0; AVL_set_inside_free( set_pointer[set_num] ); set_pointer[set_num] = NULL; }
    if(command==6){ return set_siz[set_num]; }
    if(command==7){ return AVL_set_inside_minmax(set_pointer[set_num],1); }
    if(command==8){ return AVL_set_inside_minmax(set_pointer[set_num],0); }
    if(command==9){ AVL_set_inside_swap(&set_pointer[set_num],&set_pointer[val]); }
    return 0;
}

void set_print(int set_num){ set_main(-1,set_num,0); }
void set_insert(int set_num, ll val){ set_main(1,set_num,val); }
ll set_count(int set_num, ll val){ return set_main(2,set_num,val); }
void set_erase(int set_num, ll val, int is_all){ if(is_all) set_main(4,set_num,val); else set_main(3,set_num,val); }
void set_clear(int set_num){ set_main(5,set_num,0); }
ll set_size(int set_num){ return set_main(6,set_num,0); }
ll set_max(int set_num){ return set_main(7,set_num,0); }
ll set_min(int set_num){ return set_main(8,set_num,0); }
void set_swap(ll set_num1, ll set_num2){ set_main(9,set_num1,set_num2); }

/*
insert *
size *
clear *
erase *
count *
max *
min *
swap *
begin
end
merge  source の要素のキーと等価なキーの要素がある場合、その要素は source から抽出されない
lower_bound
upper_bound
*/

// ll map_main()

/*---------------------------AVL start--------------------------------*/

#pragma endregion AVL



#pragma endregion kyopuro_templates


/*---------------Union Find tree (start)----------------------------------------------------------*/

typedef struct{ ll num , par , hei ,size; } UF;
void UFmake(ll n, UF b[]){ rep(i,0,n){ b[i].par = b[i].num = i;  b[i].hei = b[i].size = 1; }  }

ll UFroot(ll a,UF b[]){ return a==b[a].par?a:UFroot(b[a].par,b); }
ll UFsame(ll x, ll y, UF b[]){ return UFroot(x,b) == UFroot(y,b); }
ll UFsize(ll x, UF b[]){ return b[UFroot(x,b)].size; }
void UFunite(ll x, ll y, UF b[]){
    ll xroot=UFroot(x,b) , yroot=UFroot(y,b) , siz=UFsize(x,b)+UFsize(y,b);
    if(b[xroot].hei > b[yroot].hei) b[yroot].par = xroot;
    else{ b[xroot].par = yroot;  b[yroot].hei = max2( b[yroot].hei , b[xroot].hei+1 );}
    b[UFroot(x,b)].size=siz;
}

/*--------------Union Find tree (end)------------------------------------------------------------*/











// char s[1151154];
ll team[115115];
void solve(){
    // fgets(s,sizeof(s),stdin); 
    ll n,m;
    ll ans=0;
    cin(&n);
    cin(&m);
    // scanf("%s",s);
    ll cost[n];
    rep(i,0,n){
        cin(&cost[i]);
    }
    UF uf[n];
    UFmake(n,uf);
    ll x,y;
    rep(i,0,m){
        cin(&x);
        cin(&y);
        if(UFsame(x,y,uf)==0) UFunite(x,y,uf);
    }
    if(n==1){
        printf("0\n"); return;
    }
    
    ll one=0,many=0,cnt=0;
    rep(i,0,n) team[i]=INF;
    rep(i,0,n){
        ll r=UFroot(i,uf);
        set_insert(0,cost[i]);
        team[r]=min2(team[r],cost[i]);
        if( set_count(1,r) == 0 ){
            set_insert(1,r);
            if(UFsize(r,uf)==1){
                one++;
            }else{
                if(many){
                    many+=UFsize(r,uf)-2;
                }else{
                    many+=UFsize(r,uf);
                }
            }
     
        }
    }

    if(n==2&&one==2){
        printf("%lld\n",cost[0]+cost[1]); return;
    }
    if(one>many){
        printf("Impossible\n"); return;            
    }

    rep(i,0,n){
        if(team[i]==INF) continue;
        ans+=team[i];
        set_erase(0,team[i],0);
        cnt++;
    }
    while(cnt!=2*(n-m-1)){
        ll v=set_min(0);
        ans+=v;
        set_erase(0,v,0);
        cnt++;
    }

    printf("%lld\n",ans);
}

int main(void){
    ll T=1;
    // cin(&T);
    rep(i,0,T){ solve(); }
    return 0;
}


/*
    while (ng + 1 < ok) {
        ll p = ng + (ok - ng) / 2;
        ll cnt = 0;
        rep(i,0,n){
            cnt += (a[i] + p - 1) / p - 1;
        }
        if (cnt <= k) ok = p; else ng = p;
    }
*/
// 10^18 2^60 3^38 5^26