5063 Just Sum It

#include<bits/stdc++.h>
using namespace std;

#define sc( x ) scanf( "%d" , &x )
#define REP( i , n ) for( int i = 0 ; i < n ; ++i )
#define clr( t , val ) memset( t , val , sizeof( t ) )

#define pb push_back
#define all( v ) v.begin() , v.end()
#define SZ( v ) ((int)(v).size())

#define mp make_pair
#define fi first
#define se second

#define MOD 1000000007LL

typedef pair< int , int > pii;
typedef long long ll;
typedef vector< int > vi;

ll C[ 105 ][ 105 ];
int F[ 15 ];
ll TEN[ 105 ];
bool used[ 105 ][ 15 ][ 15 ];
ll memo[ 105 ][ 15 ][ 15 ];
ll DP[ 105 ][ 15 ][ 15 ];

ll dp( int L , int dig , int d ){
    if( L == 0 ) return 1;
    if( dig == 10 ) return 0;

    if( used[ L ][ dig ][ d ] ) return memo[ L ][ dig ][ d ];
    used[ L ][ dig ][ d ] = 1;
    ll &dev = memo[ L ][ dig ][ d ] = 0;
    for( int i = 0 ; i <= min( F[ dig ] - (dig == d) , L ) ; ++i ) dev = ( dev + C[ L ][ i ] * dp( L - i , dig + 1 , d ) )%MOD;
    return dev;
}

int main(){
    TEN[ 0 ] = 1;
    for( int i = 1 ; i <= 100 ; ++i ) TEN[ i ] = ( TEN[ i - 1 ] * 10 )%MOD;
    REP( i , 101 ) C[ i ][ i ] = C[ i ][ 0 ] = 1;
    for( int i = 2 ; i <= 100 ; ++i )
        for( int j = 1 ; j < i ; ++j ) C[ i ][ j ] = ( C[ i - 1 ][ j - 1 ] + C[ i - 1 ][ j ] )%MOD;
    int cases;
    cin >> cases;
    REP( tc , cases ){
        ll S = 0;
        for( int i = 1 ; i <= 9 ; ++i ) {
            cin >> F[ i ];
            S += F[ i ];
        }
        clr( used , 0 );
        ll ans = 0;
        for( int i = 1 ; i <= S ; ++i ){
            for( int j = 0 ; j < i ; ++j ){
                for( int d = 1 ; d <= 9 ; ++d )
                    if( F[ d ] ){

                        //clr( used , 0 );
                        ll a = ( dp( i - 1 , 1 , d ) * TEN[ j ] )%MOD;
                        ans = ( ans + a * (ll)d )%MOD;

                        /*
                        for( int L = 0 ; L <= S ; ++L ) DP[ L ][ 10 ] = 0;
                        for( int dig = 1 ; dig <= 10 ; ++dig ) DP[ 0 ][ dig ] = 1;

                        for( int L = 1 ; L <= i ; ++L )
                            for( int dig = 9 ; dig >= 1 ; --dig ){
                                DP[ L ][ dig ] = 0;
                                for( int k = 0 ; k <= min( F[ dig ] , L ) ; ++k ) DP[ L ][ dig ] = ( DP[ L ][ dig ] + C[ L ][ k ] * DP[ L - k ][ dig + 1 ] )%MOD;
                            }
                        ll a = ( DP[ i - 1 ][ 1 ] * TEN[ j ] )%MOD;
                        ans = ( ans + a * (ll)d )%MOD;
                        */

                    }
            }
        }
        cout << ans << '\n';
    }
}