#include using namespace std; using ll = long long; // 参考: http://kazuma8128.hatenablog.com/entry/2017/12/29/081929 template struct LazySegmentTree { using Tm = typename MonoidOp::Tm; using To = typename MonoidOp::To; int n; int h; vector data; vector lazy; LazySegmentTree() {} LazySegmentTree(int size, Tm initial_data_value = MonoidOp::unit()) { n = 1; h = 0; while (n < size) { h++; n <<= 1; } data.assign((n << 1), initial_data_value); lazy.assign((n << 1), MonoidOp::op_unit()); if (initial_data_value != MonoidOp::unit()) { for (int i = n - 1; i > 0; i--) data[i] = MonoidOp::merge(data[(i << 1)], data[(i << 1) + 1]); } } LazySegmentTree(const vector& v) { int size = v.size(); n = 1; h = 0; while (n < size) { h++; n <<= 1; } data.assign((n << 1), MonoidOp::unit()); lazy.assign((n << 1), MonoidOp::op_unit()); for (int i = 0; i < size; i++) data[i + n] = v[i]; for (int i = n - 1; i > 0; i--) data[i] = MonoidOp::merge(data[(i << 1)], data[(i << 1) + 1]); } // https://komiyam.hatenadiary.org/entry/20131202/1385992406 inline int getSegLen(int k) { return n / (1 << (31 - __builtin_clz(k))); } Tm getLeaf(int k) { return query(k, k + 1); } void push(int k) { if (lazy[k] == MonoidOp::op_unit()) return; int seg_len = getSegLen(k); data[k] = MonoidOp::apply(data[k], lazy[k], seg_len); if (seg_len > 1) { lazy[(k << 1)] = MonoidOp::op_merge(lazy[(k << 1)], lazy[k]); lazy[(k << 1) + 1] = MonoidOp::op_merge(lazy[(k << 1) + 1], lazy[k]); } lazy[k] = MonoidOp::op_unit(); } void update(int k) { Tm vl = MonoidOp::apply(data[(k << 1)], lazy[(k << 1)], getSegLen(k << 1)); Tm vr = MonoidOp::apply(data[(k << 1) + 1], lazy[(k << 1) + 1], getSegLen((k << 1) + 1)); data[k] = MonoidOp::merge(vl, vr); } //区間[a, b)に対する更新 void update(int a, int b, To x) { a += n, b += n - 1; for (int i = h; i > 0; i--) { push(a >> i); push(b >> i); } for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) { if (l & 1) lazy[l] = MonoidOp::op_merge(lazy[l], x), l++; if (r & 1) --r, lazy[r] = MonoidOp::op_merge(lazy[r], x); } while (a >>= 1, b >>= 1, a) { if (lazy[a] == MonoidOp::op_unit()) update(a); if (lazy[b] == MonoidOp::op_unit()) update(b); } } //区間[a, b)に対するクエリに答える Tm query(int a, int b) { a += n, b += n - 1; for (int i = h; i > 0; i--) { push(a >> i); push(b >> i); } Tm vl = MonoidOp::unit(), vr = MonoidOp::unit(); for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) { if (l & 1) { vl = MonoidOp::merge(vl, MonoidOp::apply(data[l], lazy[l], getSegLen(l))); l++; } if (r & 1) { --r; vr = MonoidOp::merge(MonoidOp::apply(data[r], lazy[r], getSegLen(r)), vr); } } return MonoidOp::merge(vl, vr); } }; // 以下、MonoidOpの例 template struct RangeSumAdd { using Tm = U; using To = V; static Tm merge(Tm x, Tm y) { return x + y; } static To op_merge(To x, To y) { return x + y; } static Tm apply(Tm vm, To vo, int seg_len) { return vm + vo * seg_len; } static constexpr Tm unit() { return Tm(0); } static constexpr To op_unit() { return To(0); } }; template struct RangeMinUpdate { using Tm = U; using To = V; static Tm merge(Tm x, Tm y) { return min(x, y); } static To op_merge(To x, To y) { return y; } static Tm apply(Tm vm, To vo, int seg_len) { return vo == op_unit() ? vm : vo; } static constexpr Tm unit() { return true; } static constexpr To op_unit() { return true; } }; // 作用素の初期値は更新クエリで与えられる値の定義域の範囲外の値にする template struct RangeSumUpdate { using Tm = U; using To = V; static Tm merge(Tm x, Tm y) { return x + y; } static To op_merge(To x, To y) { return y; } static Tm apply(Tm vm, To vo, int seg_len) { return vo == op_unit() ? vm : vo * seg_len; } static constexpr Tm unit() { return Tm(0); } static constexpr To op_unit() { return numeric_limits::min(); } }; // 初期値 != 単位元 の場合に注意 template struct RangeMinAdd { using Tm = U; using To = V; static Tm merge(Tm x, Tm y) { return min(x, y); } static To op_merge(To x, To y) { return x + y; } static Tm apply(Tm vm, To vo, int seg_len) { return vm + vo; } static constexpr Tm unit() { return numeric_limits::max(); } static constexpr To op_unit() { return To(0); } }; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; ll x; cin >> n >> x; vector a(n), sum(n + 1, 0); using Seg = LazySegmentTree< RangeSumUpdate >; vector st_row(n + 1, Seg(n + 1)), st_col(n + 1, Seg(n + 1)); for (int i = 0; i < n; ++i) { cin >> a[i]; sum[i + 1] = sum[i] + a[i]; st_row[i].update(i, i + 1, 1); st_col[i].update(i, i + 1, 1); } for (int d = 1; d < n; ++d) { for (int i = 0; i <= n - d; ++i) { if (st_row[i].query(i + d, i + d + 1) || st_col[i + d].query(i, i + 1)) continue; { int idx = lower_bound(sum.begin(), sum.begin() + i, sum[i] - x) - sum.begin(); if (idx < i) st_col[i + d].update(idx, i, true); } { int idx = upper_bound(sum.begin() + i + d, sum.end(), x + sum[i + d]) - sum.begin(); if (i + d < idx) st_row[i].update(i + d, idx, true); } } } cout << ((st_row[0].query(n, n + 1) > 0 || st_col[n].query(0, 1) > 0) ? "A" : "B") << "\n"; return 0; }