//线段树
;(function () {
    var parent = function (node) {
        return Math.floor(node / 2);
    };

    var Int32Array = window.Int32Array || function (size) {
            var xs = [];
            for (var i = size - 1; i >= 0; --i) {
                xs[i] = 0;
            }
            return xs;
        };

    var ceilLog2 = function (x) {
        var y = 1;
        while (y < x) {
            y *= 2;
        }
        return y;
    };

    BI.PrefixIntervalTree = function (xs) {
        this._size = xs.length;
        this._half = ceilLog2(this._size);
        this._heap = new Int32Array(2 * this._half);

        var i;
        for (i = 0; i < this._size; ++i) {
            this._heap[this._half + i] = xs[i];
        }

        for (i = this._half - 1; i > 0; --i) {
            this._heap[i] = this._heap[2 * i] + this._heap[2 * i + 1];
        }
    };

    BI.PrefixIntervalTree.prototype = {
        constructor: BI.PrefixIntervalTree,
        set: function (index, value) {
            var node = this._half + index;
            this._heap[node] = value;

            node = parent(node);
            for (; node !== 0; node = parent(node)) {
                this._heap[node] =
                    this._heap[2 * node] + this._heap[2 * node + 1];
            }
        },

        get: function (index) {
            var node = this._half + index;
            return this._heap[node];
        },

        getSize: function () {
            return this._size;
        },

        /**
         * get(0) + get(1) + ... + get(end - 1).
         */
        sumUntil: function (end) {
            if (end === 0) {
                return 0;
            }

            var node = this._half + end - 1;
            var sum = this._heap[node];
            for (; node !== 1; node = parent(node)) {
                if (node % 2 === 1) {
                    sum += this._heap[node - 1];
                }
            }

            return sum;
        },

        /**
         * get(0) + get(1) + ... + get(inclusiveEnd).
         */
        sumTo: function (inclusiveEnd) {
            return this.sumUntil(inclusiveEnd + 1);
        },

        /**
         * sum get(begin) + get(begin + 1) + ... + get(end - 1).
         */
        sum: function (begin, end) {
            return this.sumUntil(end) - this.sumUntil(begin);
        },

        /**
         * Returns the smallest i such that 0 <= i <= size and sumUntil(i) <= t, or
         * -1 if no such i exists.
         */
        greatestLowerBound: function (t) {
            if (t < 0) {
                return -1;
            }

            var node = 1;
            if (this._heap[node] <= t) {
                return this._size;
            }

            while (node < this._half) {
                var leftSum = this._heap[2 * node];
                if (t < leftSum) {
                    node = 2 * node;
                } else {
                    node = 2 * node + 1;
                    t -= leftSum;
                }
            }

            return node - this._half;
        },

        /**
         * Returns the smallest i such that 0 <= i <= size and sumUntil(i) < t, or
         * -1 if no such i exists.
         */
        greatestStrictLowerBound: function (t) {
            if (t <= 0) {
                return -1;
            }

            var node = 1;
            if (this._heap[node] < t) {
                return this._size;
            }

            while (node < this._half) {
                var leftSum = this._heap[2 * node];
                if (t <= leftSum) {
                    node = 2 * node;
                } else {
                    node = 2 * node + 1;
                    t -= leftSum;
                }
            }

            return node - this._half;
        },

        /**
         * Returns the smallest i such that 0 <= i <= size and t <= sumUntil(i), or
         * size + 1 if no such i exists.
         */
        leastUpperBound: function (t) {
            return this.greatestStrictLowerBound(t) + 1;
        },

        /**
         * Returns the smallest i such that 0 <= i <= size and t < sumUntil(i), or
         * size + 1 if no such i exists.
         */
        leastStrictUpperBound: function (t) {
            return this.greatestLowerBound(t) + 1;
        }
    };

    BI.PrefixIntervalTree.uniform = function (size, initialValue) {
        var xs = [];
        for (var i = size - 1; i >= 0; --i) {
            xs[i] = initialValue;
        }

        return new BI.PrefixIntervalTree(xs);
    };

    BI.PrefixIntervalTree.empty = function () {
        return BI.PrefixIntervalTree.uniform(size, 0);
    };

})();