Difference array

For an array

a

, its difference array stores

d_{0} = a_{0}

and

d_{i} = a_{i} - a_{i - 1}

for

i > 0

. The original entries are prefix sums of

d

. Adding

v

on indices

[l, r]

requires only

d_{l} + = v

and, when present,

d_{r + 1} - = v

.

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