// #pragma GCC target("avx") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; #define rep(i,n) for(int i = 0; i < (int)n; i++) #define FOR(n) for(int i = 0; i < (int)n; i++) #define repi(i,a,b) for(int i = (int)a; i < (int)b; i++) #define all(x) x.begin(),x.end() //#define mp make_pair #define vi vector #define vvi vector #define vvvi vector #define vvvvi vector #define pii pair #define vpii vector> template bool chmax(T &a, const T b) {if(a bool chmin(T &a, const T b) {if(a>b) {a=b; return true;} else {return false;}} using ll = long long; using ld = long double; using ull = unsigned long long; const ll INF = 1e10; const ld pi = 3.1415926535897932384626433832795028; const ll mod = 998244353; int dx[] = {1, 0, -1, 0, -1, -1, 1, 1}; int dy[] = {0, 1, 0, -1, -1, 1, -1, 1}; #define int long long void solve() { int n, m; cin >> n >> m; vi l(n), r(n); int l_sum = 0, r_sum = 0; FOR(n) { cin >> l[i]; l_sum += l[i]; } FOR(n) { cin >> r[i]; r_sum += r[i]; } if(m < l_sum || r_sum < m) { cout << -1 << endl; return; } // xを一つ増やすと、今まで入れた個数-cnt[x]だけ転倒数が増える //→xを3つ増やす場合は3*(今まで-cnt[x])。 // {cnt[x], nxt, how_many, remain} int left = 0, right = INF; while(right-left > 1) { int mid = (left + right) / 2; int cur = 0; FOR(n) { cur += max(l[i], min(mid, r[i])); } // cout << mid << " " << cur << endl; if(cur >= m) right = mid; else left = mid; } // 後はright or right-1個まで使う数を増やしていく。 int need = 0; FOR(n) need += max(l[i], min(right, r[i])); int no_need = need-m; int ans = 0; int cur_sum = 0; // for(int i = n-1; i >= 0; i--) { // ans += l[i]*cur_sum; // cur_sum += l[i]; // } map mp; FOR(n) { int use = max(l[i], min(right, r[i])); if(use == 0) continue; ++mp[0]; if(use>l[i] && use == right && no_need > 0) { --use; --no_need; } --mp[use]; } // for(auto e : mp) { // cout << e.first << " " << e.second << endl; // } int num = 0, pre = -1; for(auto e : mp) { if(pre != -1 && num != 0) { ans += (cur_sum-pre)*((num-1)*(e.first-pre)+1) + ((num-1)*(e.first-pre))*((num-1)*(e.first-pre)+1)/2 +(cur_sum-pre)*(e.first-pre-1)+(num-1)*(e.first-pre-1)*(e.first-pre)/2; } // cout << e.first << " " << ans << endl; cur_sum += num*(e.first-pre); num += e.second; pre = e.first; } cout << ans << endl; // cout << right << " " << need << " " << cur_sum << " " << no_need << endl; /* cur_sum-pre, cur_sum-pre+1, ... , cur_sum-pre+num-1, cur_sum-pre+num-1, cur_sum-pre+num, ... , cur_sum-pre+2*num-2 cur_sum-pre, ... , cur_sum-pre+(num-1)*(e.first-pre) +cur_sum-pre+num-1+cur_sum-pre+2(num-1)+...+cur_sum-pre+(e.first-pre-1) = (cur_sum-pre)*((num-1)*(e.first-pre)+1) + ((num-1)*(e.first-pre))*((num-1)*(e.first-pre)+1)/2 +(cur_sum-pre)*(e.first-pre-1)+(num-1)*(e.first-pre-1)*(e.first-pre)/2; */ } signed main() { cin.tie(nullptr); ios::sync_with_stdio(false); int t; cin >> t; while(t--) solve(); return 0; }