#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++) #define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--) #define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++) #define pers(x, s) for(ll x = (ll)(s).size()-1; (x) >= 0; (x)--) #define chmin(x, y) (x) = min((x), (y)) #define chmax(x, y) (x) = max((x), (y)) #define sz(x) ((ll)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define outl(...) dump_func(__VA_ARGS__) #define outf(x) cout << fixed << setprecision(16) << (x) << endl #define pb push_back #define fi first #define se second #define inf 2e18 #define eps 1e-9 const double PI = 3.1415926535897932384626433; using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair P; struct edge{ ll to, cost; edge(){} edge(ll a, ll b){ to = a, cost = b;} }; const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1}; const int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dy8[] = {0, -1, -1, -1, 0, 1, 1, 1}; const int mod = 998244353; //const int mod = 1000000007; struct mint{ int x; mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;} mint(const mint &ope) {x = ope.x;} mint operator-(){return mint(-x);} mint operator+(const mint &ope){return mint(x) += ope;} mint operator-(const mint &ope){return mint(x) -= ope;} mint operator*(const mint &ope){return mint(x) *= ope;} mint operator/(const mint &ope){return mint(x) /= ope;} mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;} mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;} mint& operator*=(const mint &ope){ll tmp = x; tmp *= ope.x, tmp %= mod; x = tmp; return *this;} mint& operator/=(const mint &ope){ ll n = mod-2; mint mul = ope; while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;} return *this; } mint inverse(){return mint(1) / *this;} bool operator ==(const mint &ope){return x == ope.x;} bool operator !=(const mint &ope){return x != ope.x;} bool operator <(const mint &ope)const{return x < ope.x;} }; mint modpow(mint a, ll n){ if(n == 0) return mint(1); if(n % 2) return a * modpow(a, n-1); else return modpow(a*a, n/2); } istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope = mint(t); return is;} ostream& operator <<(ostream &os, mint &ope){return os << ope.x;} ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;} ll modpow(ll a, ll n, ll mod){ if(n == 0) return 1; if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod; else return modpow((a*a)%mod, n/2, mod) % mod; } vector fact, fact_inv; void make_fact(int n){ fact.resize(n+1), fact_inv.resize(n+1); fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i); fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1); } mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];} mint perm(int n, int k){ return comb(n, k) * fact[k]; } mint divide(int n, int k){ if(n == 0 && k == 0) return 1; return comb(n+k-1, k-1); } template T comb2(ll n, ll k){ if(n < 0 || k < 0 || n < k) return T(0); T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;} vector prime, pvec, qrime; void make_prime(int n){ prime.resize(n+1); rep(i, 2, n){ if(prime[i] == 0) pvec.push_back(i), prime[i] = i; for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;} } } void make_qrime(int n){ qrime.resize(n+1); rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];} } void factorize(ll n, map &mp){ mp.clear(); for(auto p : pvec) while(n % p == 0) mp[p]++, n /= p; if(n > 1) mp[n]++; } bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;} void mark(){ cout << "*" << endl; } void yes(){ cout << "Yes" << endl; } void no(){ cout << "No" << endl; } ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); } ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); } ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;} ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;} ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);} ll lcm(ll a, ll b){return a/gcd(a, b)*b;} template T arith(T x){return x*(x+1)/2;} template T arith2(T x){return x*(x+1)*(x*2+1)/6;} ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;} ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;} string lltos(ll x, ll b = 10){if(x == 0) return "0"; string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;} ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;} template void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());} int popcount(ull x){ x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL); return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56; } template vector> rle(vector vec){ vector> ret; for(auto x : vec){if(sz(ret) == 0 || ret.back().first != x) ret.push_back(P(x, 1)); else ret.back().second++;} return ret; } vector> rle(string s){ vector vec; for(auto c : s) vec.push_back(c); return rle(vec);} template pair& operator+=(pair &s, const pair &t){s.first += t.first, s.second += t.second; return s;} template pair& operator-=(pair &s, const pair &t){s.first -= t.first, s.second -= t.second; return s;} template pair operator+(const pair &s, const pair &t){return pair(s.first+t.first, s.second+t.second);} template pair operator-(const pair &s, const pair &t){return pair(s.first-t.first, s.second-t.second);} template T dot(const pair &s, const pair &t){return s.first*t.first + s.second*t.second;} template T cross(const pair &s, const pair &t){return s.first*t.second - s.second*t.first;} template T mdist(pair s, pair t){return abs(s.first-t.first) + abs(s.second-t.second);} template T cdist(pair s, pair t){return max(abs(s.first-t.first), abs(s.second-t.second));} template T edist2(pair s, pair t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);} template ostream& operator << (ostream& os, vector& vec){reps(i, vec) os << vec[i] << " "; return os;} template ostream& operator << (ostream& os, const vector& vec){reps(i, vec) os << vec[i] << " "; return os;} template ostream& operator << (ostream& os, list& ls){for(auto x : ls) os << x << " "; return os;} template ostream& operator << (ostream& os, const list& ls){for(auto x : ls) os << x << " "; return os;} template ostream& operator << (ostream& os, deque& deq){reps(i, deq) os << deq[i] << " "; return os;} template ostream& operator << (ostream& os, pair& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;} template ostream& operator << (ostream& os, const pair& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;} template ostream& operator << (ostream& os, map& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;} template ostream& operator << (ostream& os, set& ope){for(auto x : ope) os << x << " "; return os;} template ostream& operator << (ostream& os, multiset& ope){for(auto x : ope) os << x << " "; return os;} template void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;} template ostream& operator << (ostream& os, array& arr){reps(i, arr) os << arr[i] << " "; return os;} template ostream& operator << (ostream& os, const array& arr){reps(i, arr) os << arr[i] << " "; return os;} void dump_func(){cout << endl;} template void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);} template void bssert(bool b, T t){ if(!b) cout << t << endl, exit(0); } struct SegTree{ typedef P SEG; int size; vector seg; SegTree(){} SegTree(int size){ this->size = size; seg.resize(1<<(size+1)); } SEG id(){ //identity element return P(0, 0); } SEG ope(SEG a, SEG b){ //operator return a+b; } void init(){ for(int i = 0; i < (1<<(size+1)); i++) seg[i] = id(); } void set(int i, SEG x){ seg[i+(1<= 1; i--) seg[i] = ope(seg[i*2], seg[i*2+1]); } void update(int i, SEG val){ i += (1 << size); seg[i] = val; while(i > 1){ i /= 2; seg[i] = ope(seg[i*2], seg[i*2+1]); } } SEG query(int a, int b, int k, int l, int r){ if(b < l || r < a) return id(); if(a <= l && r <= b) return seg[k]; SEG lval = query(a, b, k*2, l, (l+r)/2); SEG rval = query(a, b, k*2+1, (l+r)/2+1, r); return ope(lval, rval); } SEG query(ll a, ll b){ if(a > b) return id(); return query(a, b, 1, 0, (1< mp; map mp2; vector

parent; //subtree of v is [pre_order[v], back_order[v]] vector pre_order; vector back_order; int order; int global_id, local_id; vector size, depth; vector > prev; HLD(){} void predfs(vector G[], int v, int p, int d) { size[v] = 1, depth[v] = d, prev[v][0] = p; for(int i = 0; i < G[v].size(); i++){ if(G[v][i] == p) continue; predfs(G, G[v][i], v, d+1); size[v] += size[G[v][i]]; } } void maindfs(vector G[], int v, int p) { mp[v] = make_pair(global_id, local_id); mp2[make_pair(global_id, local_id)] = v; pre_order[v] = ++order; if(G[v].size() == 1 && G[v][0] == p){ back_order[v] = order; return; } vector

vec; for(int i = 0; i < G[v].size(); i++){ if(G[v][i] == p) continue; vec.push_back(make_pair(size[G[v][i]], G[v][i])); } sort(vec.rbegin(), vec.rend()); local_id++; if(vec.size() >= 1) maindfs(G, vec[0].second, v); for(int i = 1; i < vec.size(); i++){ parent.push_back(mp[v]); global_id++, local_id = 0; maindfs(G, vec[i].second, v); } back_order[v] = order; } int getLCA(int u, int v){ int x = u, y = v; if(depth[y] > depth[x]) swap(x, y); for(int i = logV-1; i >= 0; i--){ if(depth[x] - (1<= depth[y]) x = prev[x][i]; } if(x == y) return x; for(int i = logV-1; i >= 0; i--){ if(prev[x][i] != prev[y][i]){ x = prev[x][i]; y = prev[y][i]; } } x = prev[x][0]; return x; } void pathcalc(int v, int lca, vector > &dest) { int gid = mp[v].first, lid = mp[v].second; int Gid = mp[lca].first, Lid = mp[lca].second; while(Gid != gid){ dest.push_back(make_pair(gid, make_pair(0, lid))); int ngid = parent[gid].first, nlid = parent[gid].second; gid = ngid, lid = nlid; } dest.push_back(make_pair(gid, make_pair(Lid, lid))); } void init(vector G[], int V) // The tree must be undirected and 1-indexed. { this->V = V, logV = 0; for(int t = V; t; t/=2) logV++; prev.resize(V+1); for(int i = 0; i <= V; i++) prev[i].resize(logV); size.resize(V+1), depth.resize(V+1); predfs(G, 1, 0, 0); prev[0][0] = 0; for(int i = 1; i < logV; i++){ for(int j = 1; j <= V; j++){ prev[j][i] = prev[prev[j][i-1]][i-1]; } } mp.resize(V+1), mp2.clear(); parent.clear(), parent.push_back(make_pair(-1, -1)); pre_order.resize(V+1), back_order.resize(V+1); global_id = local_id = 0, order = 0; maindfs(G, 1, 0); } void path(int u, int v, vector > &dest) { dest.clear(); int lca = getLCA(u, v); pathcalc(u, lca, dest); pathcalc(v, lca, dest); pair p = make_pair(mp[lca].first, make_pair(mp[lca].second, mp[lca].second)); for(int i = 0; i < dest.size(); i++){ if(dest[i] == p){ dest.erase(dest.begin()+i); return ; } } } void getPath(int u, int v, vector

&dest) //transform an u-v path into intervals[l, r] on segtree. { vector > src; path(u, v, src); dest.clear(); for(int i = 0; i < src.size(); i++){ int u = mp2[make_pair(src[i].first, src[i].second.first)], v = mp2[make_pair(src[i].first, src[i].second.second)]; dest.push_back(make_pair(pre_order[u], pre_order[v])); } } }; ll n, Q; ll a[200005]; vector G[200005]; int main(void) { ios::sync_with_stdio(0); cin.tie(0); cin >> n >> Q; rep(i, 1, n) cin >> a[i]; ll u, v; rep(i, 1, n-1){ cin >> u >> v; G[u].pb(v), G[v].pb(u); } HLD hld; hld.init(G, n); SegTree seg(18); seg.init(); rep(i, 1, n){ ll s = a[i]; for(auto u : G[i]){ if(u == hld.prev[i][0]) continue; s += a[u]; seg.set(hld.pre_order[i], P(a[i], s)); } } seg.setup(); ll t, x; rep(i, 1, Q){ cin >> t; if(t == 0){ cin >> v >> x; a[v] += x; { ll p = hld.pre_order[v]; auto res = seg.query(p, p); res.fi += x, res.se += x; seg.update(p, res); } if(v != 1){ v = hld.prev[v][0]; ll p = hld.pre_order[v]; auto res = seg.query(p, p); res.se += x; seg.update(p, res); } } if(t == 1){ cin >> u >> v; vector

vec; hld.getPath(u, v, vec); P res = P(0, 0); for(auto p : vec) res += seg.query(p.fi, p.se); ll ans = res.se - res.fi; ll l = hld.getLCA(u, v); ans += a[l]; if(l != 1) l = hld.prev[l][0], ans += a[l]; cout << ans << "\n"; } } return 0; }